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Page 1
Algebraic Expressions
Points to remember
? Algebraic expressions are formed from variables and constants.
? A quantity having a fixed numerical value is called a constant whereas a
quantity having different numerical values is called a variable.
? Expressions are made up of terms.
? Terms which have the same algebraic factors are like terms and terms which
have different algebraic factors are unlike terms.
? Any expression with one or more terms is called a polynomial. A one term
expression is called monomial, a two-term expression is called binomial and a
three term expression is called trinomial.
? The highest power of the variable is the degree of an algebraic expression.
? Rules and formula are written in a concise and general form using algebraic
expressions.
QUESTIONS:
1. What is the coefficient of variable x
2
in the algebraic expression?
a. 7x
3
– 5x
2
+ 3
b.
?? ?? x
2
+ 9
c. 6 + 3x + 2x
2
2. Add the like terms:
- 4 ab
2
, 9 b
2
a, 7 ab
2
3. Subtract (2x – y) from (4x – 3y + 6)
4. Find the value of 7 – 55x, if x = -3.
5. Simplify: 4a(2 – b) – (2a – ab).
6. If p = - 2 and q = 3, then what will be the value of p
2
– q
2
+ pq.
7. Add: 12 xy, -20 yx, 28 xy.
Page 2
Algebraic Expressions
Points to remember
? Algebraic expressions are formed from variables and constants.
? A quantity having a fixed numerical value is called a constant whereas a
quantity having different numerical values is called a variable.
? Expressions are made up of terms.
? Terms which have the same algebraic factors are like terms and terms which
have different algebraic factors are unlike terms.
? Any expression with one or more terms is called a polynomial. A one term
expression is called monomial, a two-term expression is called binomial and a
three term expression is called trinomial.
? The highest power of the variable is the degree of an algebraic expression.
? Rules and formula are written in a concise and general form using algebraic
expressions.
QUESTIONS:
1. What is the coefficient of variable x
2
in the algebraic expression?
a. 7x
3
– 5x
2
+ 3
b.
?? ?? x
2
+ 9
c. 6 + 3x + 2x
2
2. Add the like terms:
- 4 ab
2
, 9 b
2
a, 7 ab
2
3. Subtract (2x – y) from (4x – 3y + 6)
4. Find the value of 7 – 55x, if x = -3.
5. Simplify: 4a(2 – b) – (2a – ab).
6. If p = - 2 and q = 3, then what will be the value of p
2
– q
2
+ pq.
7. Add: 12 xy, -20 yx, 28 xy.
8. Add : 49y
2
x, 12xy
2
, 11x
2
y, 32xy.
9. If x = -2, then find the value of -4x + 9 – 2x
2
.
10. What should be added to a
2
+ b
2
to get 3a
2
+ 7b.
11. Add the algebraic expressions: (-13 x + 20) and (22xy – 7y + 20x).
12. Find the value of algebraic expression (2ab + 3bc + 4ca), when a = 2, b = -1
and c = 1.
13. Evaluate
?? ?? –
?? ?? for a = 1 and b = -2.
14. Subtract (1 – 2x
2
) from (x
3
+ 5x
2
+ x + 1).
15. Simplify: 5x – [{3y – (x – 2y)}].
16. Subtract x
4
– y
4
from (2x
4
– x
2
y
2
– y
4
).
17. If x = -8, find the value of 89 – 4(11 – x).
18. What should be added to a
2
+ b
2
to get (a – b)
2
?
19. What should be added to a
2
+ b
2
- 2ab to get (a + b)
2
20. Find the value of
?? ?? p -
?? ?? q, if q- p = 32.
21. By how much is 4x
3
– 2x
2
+ 8x greater than 2x
3
– 2x
2
+ 6x?
22. Add 3x + 5 and 5x +3 and find the coefficient of x.
23. Find the product of numerical coefficient of x
2
and y in the algebraic
expression: 5x
2
+2y
2
– 7y + 2x + 9.
24. Simplify: (4ax – 3by)(4ax + 3by).
25. Find x
2
- y
2
if x = 2 and y = -2.
26. Find x
3
+ y
3
if x = 4 and y = -3.
27. Add (2x
2
– 3x + 1) to sum of (5x
2
– 3x) and (2x + 3).
28. Raju purchased a book for ? (3x + 15) and 2 copies for ? (x – 4). How much
did he spend in all?
29. If a side of an equilateral triangle is 9x units, then find the perimeter of the
triangle.
30. The perimeter of a triangle is (12x - 5) cm. If its two sides are (x- 2) cm and
(5x + 12) cm long, then what is the length of its third side?
31. If p = -2, then find the value of -2p
3
+ 4p
2
+ p.
Page 3
Algebraic Expressions
Points to remember
? Algebraic expressions are formed from variables and constants.
? A quantity having a fixed numerical value is called a constant whereas a
quantity having different numerical values is called a variable.
? Expressions are made up of terms.
? Terms which have the same algebraic factors are like terms and terms which
have different algebraic factors are unlike terms.
? Any expression with one or more terms is called a polynomial. A one term
expression is called monomial, a two-term expression is called binomial and a
three term expression is called trinomial.
? The highest power of the variable is the degree of an algebraic expression.
? Rules and formula are written in a concise and general form using algebraic
expressions.
QUESTIONS:
1. What is the coefficient of variable x
2
in the algebraic expression?
a. 7x
3
– 5x
2
+ 3
b.
?? ?? x
2
+ 9
c. 6 + 3x + 2x
2
2. Add the like terms:
- 4 ab
2
, 9 b
2
a, 7 ab
2
3. Subtract (2x – y) from (4x – 3y + 6)
4. Find the value of 7 – 55x, if x = -3.
5. Simplify: 4a(2 – b) – (2a – ab).
6. If p = - 2 and q = 3, then what will be the value of p
2
– q
2
+ pq.
7. Add: 12 xy, -20 yx, 28 xy.
8. Add : 49y
2
x, 12xy
2
, 11x
2
y, 32xy.
9. If x = -2, then find the value of -4x + 9 – 2x
2
.
10. What should be added to a
2
+ b
2
to get 3a
2
+ 7b.
11. Add the algebraic expressions: (-13 x + 20) and (22xy – 7y + 20x).
12. Find the value of algebraic expression (2ab + 3bc + 4ca), when a = 2, b = -1
and c = 1.
13. Evaluate
?? ?? –
?? ?? for a = 1 and b = -2.
14. Subtract (1 – 2x
2
) from (x
3
+ 5x
2
+ x + 1).
15. Simplify: 5x – [{3y – (x – 2y)}].
16. Subtract x
4
– y
4
from (2x
4
– x
2
y
2
– y
4
).
17. If x = -8, find the value of 89 – 4(11 – x).
18. What should be added to a
2
+ b
2
to get (a – b)
2
?
19. What should be added to a
2
+ b
2
- 2ab to get (a + b)
2
20. Find the value of
?? ?? p -
?? ?? q, if q- p = 32.
21. By how much is 4x
3
– 2x
2
+ 8x greater than 2x
3
– 2x
2
+ 6x?
22. Add 3x + 5 and 5x +3 and find the coefficient of x.
23. Find the product of numerical coefficient of x
2
and y in the algebraic
expression: 5x
2
+2y
2
– 7y + 2x + 9.
24. Simplify: (4ax – 3by)(4ax + 3by).
25. Find x
2
- y
2
if x = 2 and y = -2.
26. Find x
3
+ y
3
if x = 4 and y = -3.
27. Add (2x
2
– 3x + 1) to sum of (5x
2
– 3x) and (2x + 3).
28. Raju purchased a book for ? (3x + 15) and 2 copies for ? (x – 4). How much
did he spend in all?
29. If a side of an equilateral triangle is 9x units, then find the perimeter of the
triangle.
30. The perimeter of a triangle is (12x - 5) cm. If its two sides are (x- 2) cm and
(5x + 12) cm long, then what is the length of its third side?
31. If p = -2, then find the value of -2p
3
+ 4p
2
+ p.
32. The length of three sides of a triangle (in cm) are 6a - 3, 5a + 2 and 6a + 5.
Find the perimeter of the triangle, if a = 2.
33. Find the area of the rectangle, if x = 2.
34. Base of the triangle is 6x cm and its height is 5y cm, find the area of
the triangle.
35. Find the perimeter of a regular pentagon whose side is 3a cm.
Page 4
Algebraic Expressions
Points to remember
? Algebraic expressions are formed from variables and constants.
? A quantity having a fixed numerical value is called a constant whereas a
quantity having different numerical values is called a variable.
? Expressions are made up of terms.
? Terms which have the same algebraic factors are like terms and terms which
have different algebraic factors are unlike terms.
? Any expression with one or more terms is called a polynomial. A one term
expression is called monomial, a two-term expression is called binomial and a
three term expression is called trinomial.
? The highest power of the variable is the degree of an algebraic expression.
? Rules and formula are written in a concise and general form using algebraic
expressions.
QUESTIONS:
1. What is the coefficient of variable x
2
in the algebraic expression?
a. 7x
3
– 5x
2
+ 3
b.
?? ?? x
2
+ 9
c. 6 + 3x + 2x
2
2. Add the like terms:
- 4 ab
2
, 9 b
2
a, 7 ab
2
3. Subtract (2x – y) from (4x – 3y + 6)
4. Find the value of 7 – 55x, if x = -3.
5. Simplify: 4a(2 – b) – (2a – ab).
6. If p = - 2 and q = 3, then what will be the value of p
2
– q
2
+ pq.
7. Add: 12 xy, -20 yx, 28 xy.
8. Add : 49y
2
x, 12xy
2
, 11x
2
y, 32xy.
9. If x = -2, then find the value of -4x + 9 – 2x
2
.
10. What should be added to a
2
+ b
2
to get 3a
2
+ 7b.
11. Add the algebraic expressions: (-13 x + 20) and (22xy – 7y + 20x).
12. Find the value of algebraic expression (2ab + 3bc + 4ca), when a = 2, b = -1
and c = 1.
13. Evaluate
?? ?? –
?? ?? for a = 1 and b = -2.
14. Subtract (1 – 2x
2
) from (x
3
+ 5x
2
+ x + 1).
15. Simplify: 5x – [{3y – (x – 2y)}].
16. Subtract x
4
– y
4
from (2x
4
– x
2
y
2
– y
4
).
17. If x = -8, find the value of 89 – 4(11 – x).
18. What should be added to a
2
+ b
2
to get (a – b)
2
?
19. What should be added to a
2
+ b
2
- 2ab to get (a + b)
2
20. Find the value of
?? ?? p -
?? ?? q, if q- p = 32.
21. By how much is 4x
3
– 2x
2
+ 8x greater than 2x
3
– 2x
2
+ 6x?
22. Add 3x + 5 and 5x +3 and find the coefficient of x.
23. Find the product of numerical coefficient of x
2
and y in the algebraic
expression: 5x
2
+2y
2
– 7y + 2x + 9.
24. Simplify: (4ax – 3by)(4ax + 3by).
25. Find x
2
- y
2
if x = 2 and y = -2.
26. Find x
3
+ y
3
if x = 4 and y = -3.
27. Add (2x
2
– 3x + 1) to sum of (5x
2
– 3x) and (2x + 3).
28. Raju purchased a book for ? (3x + 15) and 2 copies for ? (x – 4). How much
did he spend in all?
29. If a side of an equilateral triangle is 9x units, then find the perimeter of the
triangle.
30. The perimeter of a triangle is (12x - 5) cm. If its two sides are (x- 2) cm and
(5x + 12) cm long, then what is the length of its third side?
31. If p = -2, then find the value of -2p
3
+ 4p
2
+ p.
32. The length of three sides of a triangle (in cm) are 6a - 3, 5a + 2 and 6a + 5.
Find the perimeter of the triangle, if a = 2.
33. Find the area of the rectangle, if x = 2.
34. Base of the triangle is 6x cm and its height is 5y cm, find the area of
the triangle.
35. Find the perimeter of a regular pentagon whose side is 3a cm.
36. Find the area of a square whose side is 3ab.
37. In the given figure, rectangular length is 7x cm and its breadth is 3y cm, find
its perimeter.
38. Find the perimeter of a square whose side is 9ab cm.
39. Find the perimeter of a circle whose radius is 3x cm.
Page 5
Algebraic Expressions
Points to remember
? Algebraic expressions are formed from variables and constants.
? A quantity having a fixed numerical value is called a constant whereas a
quantity having different numerical values is called a variable.
? Expressions are made up of terms.
? Terms which have the same algebraic factors are like terms and terms which
have different algebraic factors are unlike terms.
? Any expression with one or more terms is called a polynomial. A one term
expression is called monomial, a two-term expression is called binomial and a
three term expression is called trinomial.
? The highest power of the variable is the degree of an algebraic expression.
? Rules and formula are written in a concise and general form using algebraic
expressions.
QUESTIONS:
1. What is the coefficient of variable x
2
in the algebraic expression?
a. 7x
3
– 5x
2
+ 3
b.
?? ?? x
2
+ 9
c. 6 + 3x + 2x
2
2. Add the like terms:
- 4 ab
2
, 9 b
2
a, 7 ab
2
3. Subtract (2x – y) from (4x – 3y + 6)
4. Find the value of 7 – 55x, if x = -3.
5. Simplify: 4a(2 – b) – (2a – ab).
6. If p = - 2 and q = 3, then what will be the value of p
2
– q
2
+ pq.
7. Add: 12 xy, -20 yx, 28 xy.
8. Add : 49y
2
x, 12xy
2
, 11x
2
y, 32xy.
9. If x = -2, then find the value of -4x + 9 – 2x
2
.
10. What should be added to a
2
+ b
2
to get 3a
2
+ 7b.
11. Add the algebraic expressions: (-13 x + 20) and (22xy – 7y + 20x).
12. Find the value of algebraic expression (2ab + 3bc + 4ca), when a = 2, b = -1
and c = 1.
13. Evaluate
?? ?? –
?? ?? for a = 1 and b = -2.
14. Subtract (1 – 2x
2
) from (x
3
+ 5x
2
+ x + 1).
15. Simplify: 5x – [{3y – (x – 2y)}].
16. Subtract x
4
– y
4
from (2x
4
– x
2
y
2
– y
4
).
17. If x = -8, find the value of 89 – 4(11 – x).
18. What should be added to a
2
+ b
2
to get (a – b)
2
?
19. What should be added to a
2
+ b
2
- 2ab to get (a + b)
2
20. Find the value of
?? ?? p -
?? ?? q, if q- p = 32.
21. By how much is 4x
3
– 2x
2
+ 8x greater than 2x
3
– 2x
2
+ 6x?
22. Add 3x + 5 and 5x +3 and find the coefficient of x.
23. Find the product of numerical coefficient of x
2
and y in the algebraic
expression: 5x
2
+2y
2
– 7y + 2x + 9.
24. Simplify: (4ax – 3by)(4ax + 3by).
25. Find x
2
- y
2
if x = 2 and y = -2.
26. Find x
3
+ y
3
if x = 4 and y = -3.
27. Add (2x
2
– 3x + 1) to sum of (5x
2
– 3x) and (2x + 3).
28. Raju purchased a book for ? (3x + 15) and 2 copies for ? (x – 4). How much
did he spend in all?
29. If a side of an equilateral triangle is 9x units, then find the perimeter of the
triangle.
30. The perimeter of a triangle is (12x - 5) cm. If its two sides are (x- 2) cm and
(5x + 12) cm long, then what is the length of its third side?
31. If p = -2, then find the value of -2p
3
+ 4p
2
+ p.
32. The length of three sides of a triangle (in cm) are 6a - 3, 5a + 2 and 6a + 5.
Find the perimeter of the triangle, if a = 2.
33. Find the area of the rectangle, if x = 2.
34. Base of the triangle is 6x cm and its height is 5y cm, find the area of
the triangle.
35. Find the perimeter of a regular pentagon whose side is 3a cm.
36. Find the area of a square whose side is 3ab.
37. In the given figure, rectangular length is 7x cm and its breadth is 3y cm, find
its perimeter.
38. Find the perimeter of a square whose side is 9ab cm.
39. Find the perimeter of a circle whose radius is 3x cm.
40. Perimeter of a square is 28x cm. Find its area.
41. Simplify: 16a
2
b + 9ba
2
+ 3a
2
b – 4a
2
b and find the numerical coefficient of the
resultant algebraic expression.
42. Simplify: (- 4a + 5x)(5x + 4a).
43. Find: (a+ b)(a – b) if a = 7 and b = -6
44. Evaluate: 5ab + 4a
2
– 2b
2
for a =1 and b = -1.
45. Write an algebraic expression for the following:
7 is added to the product of two numbers 2x and 3y.
46. Simplify: 7x + [5x – (2 – x) + 2]
47. Simplify: -2a
2
+ (2a – b)(a + b) + 2ba + b
2
.
48. Write an algebraic expression for:
5 is subtracted from the sum of x and y.
49. Find the n
th
term of the number pattern 6, 11, 16, 21, ………………….
50. Find the n
th
term of the number pattern 4, 8, 12, 16, …………………..
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FAQs on Mental Maths Questions and Answers: Algebric Expressions - Mental Math for Class 7
| 1. What are algebraic expressions? |  |
Ans. Algebraic expressions are mathematical phrases that contain variables, constants, and arithmetic operations. They can represent quantities and relationships in a concise and abstract way.
| 2. How do you simplify algebraic expressions? | |
Ans. To simplify algebraic expressions, combine like terms by adding or subtracting coefficients of the same variables. Also, apply the rules of arithmetic operations such as multiplication and division.
| 3. What is the difference between an algebraic expression and an algebraic equation? | |
Ans. An algebraic expression is a mathematical phrase that consists of variables, constants, and arithmetic operations, whereas an algebraic equation is a statement that asserts the equality of two algebraic expressions.
| 4. Can you give an example of an algebraic expression? | |
Ans. An example of an algebraic expression is 3x + 2y - 5, where x and y are variables, and 3, 2, and 5 are constants.
| 5. How are algebraic expressions used in real-life situations? | |
Ans. Algebraic expressions are used in various real-life situations such as calculating the cost of items, determining the amount of ingredients needed for a recipe, and analyzing patterns in data.
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