NCERT Solutions: Algebraic Expressions

# NCERT Solutions for Class 8 Maths - Algebraic Expressions- 1

## Exercise 10.1

Q.1. Get the algebraic expressions in the following cases using variables, constants, and arithmetic operations:
(i) Subtraction of z from y.

Ans: y - z

(ii) One-half of the sum of numbers x and y.

Ans: (x + y)/2

(iii) The number z multiplied by itself.

Ans: Z2

(iv) One-fourth of the product of numbers p and q.

Ans: pq/4

(v) Numbers x and y both squared and added.

Ans: x2 + y2

(vi) Number 5 added to three times the product of m and n.

Ans: 3mn + 5

(vii) A product of numbers y and z subtracted from 10.

Ans: 10 - yz

(viii) Sum of numbers a and b subtracted from their product.

Ans: ab - (a + b)

Q.2. (i) Identify the terms and their factors in the following expressions, show the terms and factors by tree diagram:
(a) x - 3

Ans:

(b) 1 + x + x2

Ans:

(c) y - y3

Ans:

(d) 5xy2 + 7x2y

Ans:

(e) -ab + 2b2 - 3a2

Ans:

(ii) Identify the terms and factors in the expressions given below:

(a) -4x + 5

Ans:
Terms: -4x,5
Factors: -4,x ; 5

(b) -4x + 5y

Ans:
Terms: -4x, 5y
Factors: -4,x ; 5,y

(c) 5y + 3y2

Ans:
Terms: 5y,3y2
Factors: 5, y ; 3,y,y

(d) xy + 2x2y2

Ans:

Terms: xy, 2x2y2
Factors: x, y ; 2x, x, y, y

(e) pq + q

Ans:

Terms: pq, q
Factors: p, q ; q

(f) 1.2ab - 2.4b + 3.6a

Ans:

Terms: 1,2ab.-2.4b,3 6a

Factors: 1.2.a.b ; -2.4,6 ; 3.6,a

(g)

Ans:

(h) 0.1 p2 + 0.2q2

Ans:
Terms: 0.1 p2,0.2q2
Factors: 0. 1,p,p, ; 0.2, q,q

Q.3. Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) 5 - 3t2
(ii) 1 + t + t2 + t2
(iii) x + 2xy + 3y
(iv) 100m + 1000n
(v) -p2q2 + 7pq
(vi) 1.2a + 0.8b
(vii) 3.14 r2
(viii) 2(l + b)
(ix) 0.1y + 0.01y
2

Ans:

Q.4. (a) Identify terms which contain x and give the coefficient of x.
(i) y2x + y
(ii) 13y2 - 8yx
(iii) x + y + 2
(iv) 5 + z + zx
(v) 1 + x + xy
(vi) 12xy2 + x25
(vii) 7x + xy2

Ans:

(b) Identify terms which contain y2 and give the coefficient of y2.
(i) 8 - xy2
(ii) 5y2 + 7x
(iii) 2x2y - 15xy2 + 7y
2

Ans:

Q.5. Classify into monomials, binomials and trinomials:
(i) 4y - 7x
(ii) y2
(iii) x + y - xy
(iv) 100
(v) ab - a - b
(vi) 5 - 3t
(vii) 4p2q - 4pq2
(viii) 7mn
(ix) z2 - 3z + 8
(x) a2 + b2
(xi) z2 + z

(xii) 1 + x + x2

Ans:

Q.6. State whether a given pair of terms is of like or unlike terms:

(i) 1,100
(ii)

(iii) -29x, -29y
(iv) 14xy, 42 yx
(v) 4m2p, 4mp2
(vi) 12xz, 12x2 z2

Ans:

Q.7. Identify like terms in the following:
(a) -xy2, -4yx2, 8x2, 2xy2, 7y,  -11x2  - 100x, - 11yx, 20x2y, -6x2, y, 2xy, 3x

Ans: Like terms are:

(i) -xy2,2 xy2
(ii) -4yx2 , 20x2y
(iii) 8x2,-11x2,-6x2
(iv) 7y, y
(v) -100x, 3x
(vi) -11yx, 2xy

(b) 10pq, 7p, 8q, -p2q2, -7qp, -100q, -23, 12q2p2, -5p2, 41,2405 p, 78qp, 13p2q, qp2, 701p2

Ans: Like terms are:

(i) 10 pq - 7 pq,78 pq
(ii) 7p, 2405 p
(iii) 8q,- 100q
(iv) -p2q2, 12p2q2
(v) -12,41
(vi)
-5p2,701p2
(vii) 13 p2q,qp2

## Exercise 10.2

Q1: If m = 2, find the value of:
(i) m - 2
(ii) 3m - 5
(iii) 9 - 5m
(iv) 3m2 - 2m - 7
(v)

Ans:
(i) m - 2 = 2 - 2    [Putting m = 2]
= 0

(ii) 3m - 5 = 3 x 2 - 5     [Putting m = 2]
= 6 - 5 = 1

(iii) 9 - 5m = 9 - 5 x 2    [Putting m = 2]
= 9 - 10 = - 1

(iv) 3m2 - 2m - 7
= 3(2)2 - 2 (2) - 7        [Putting m = 2]
= 3 x 4 - 2 x 2 - 7
= 12-4-7
= 12- 11 = 1

(v)       [Putting m = 2]
= 5 - 4 = 1

Q2: If p = -2, find the value of:
(i) 4p + 7
(ii) - 3p2 + 4p + 7
(iii) -2p3 - 3p2 +4/7 + 7

Ans:
(i) 4p + 7 = 4 (- 2) + 7    [Putting p= -2]
= -8 + 7 = -1

(ii) -3p2+4p + 7
= -3 (-2)2+ 4 (-2) + 7    [Putting p = - 2]
= - 3 x 4 - 8 + 7
= - 12 - 8 + 7
= -20 + 7 = -13

(iii) - 2p3 - 3p2 +4p + 7
= - 2 (-2)3 - 3(-2)+ 4 (-2) + 7     [Putting p = - 2]
= -2 x(-8)-3 x4 -8 + 7
= 16-12-8 + 7
= -20 + 23 = 3

Q3: Find the value of the following expressions, when x = -1:
(i) 2x - 7
(ii) -x + 2
(iii) x2 + 2x  + 1
(iv) 2x2- x - 2

Ans:
(i) 2x - 7 = 2 (-1) - 7      [Putting x= - 1]
= - 2 - 7 = - 9

(ii) - x + 2 = - (-1) + 2     [Putting x= - 1]
= 1 + 2 = 3

(iii) x2 + 2 x + 1 = (-1)2 + 2 (-1) + 1    [Putting x= - 1]
= 1 - 2 + 1
= 2 - 2 = 0

(iv) 2x2- x - 2 = 2 (-1)2 - (-1) - 2     [Putting x= - 1]
= 2x1 + 1-2
= 2 + 1 - 2
= 3 - 2 = 1

Q4: If a = 2,b = -2, find the value of:
(i) a2 + b
(ii) a2+ab + b2
(iii) a2 - b2

Ans:
(i) a2 + b2 ( 2)2 + (- 2)2    [Putting a = 2. b = - 2 ]
= 4 + 4 = 8

(ii) a2+ab + b
= (2) + ( 2) (- 2) +(-2)2   [Putting a = 2. b = - 2 ]
= 4 - 4 + 4 = 4

(iii) a2 - b2 = (2)2 - (-2)2  [Putting a = 2,b = - 2]
= 4 - 4 = 0

Q5: When a = 0, b = -1, find the value of the given expressions:
(i) 2a + 2b
(ii) 2a2+b2+1
(iii) 2a2b + 2ab2 +ab
(iv) a2+ab+2

Ans:
(i) 2a + 2b = 2 (0) + 2 (-1)    [Putting a - 0,b = - 1]
= 0 - 2 = -2

(ii) 2a2 + b2 + 1 = 2 (0)2 + (-1)2 + 1      [Putting a - 0,b = - 1]
= 2 x 0 + 1+ 1 = 0 + 2 = 2

(iii) 2a2b + 2ab2 + ab = 2(0)2 (-1) + 2 (0 )(-1)2 + (0 )(-1)     [Putting a - 0,b = - 1]
= 0 + 0 + 0 = 0

(iv) a2 +ab + 2 - (0)2 + (0) (-1) + 2   [Putting a - 0,b = - 1]
= 0 + 0 + 2 = 2

Q6: Simplify the expressions and find the value if x is equal to 2:
(i) x + 7 + 4 (x- 5)
(ii) 3 (x + 2) + 5x - 7
(iii) 6x + 5 (x - 2)
(iv) 4 (2x - 1) + 3x + 11

Ans:
(i) x + 7 + 4(x- 5) = x + 7 + 4x - 20 = x + 4 x + 7 - 20
= 5 x - 13 = 5 x 2 - 13                            [Putting x = 2]
= 10-13 = -3

(ii) 3 (x+ 2) + 5x - 7 = 3x + 6 + 5x -7 = 3x + 5x + 6 - 7
= 8x - 1 = 8 x 2-1                    [Putting x = -1]
= 16 - 1 = 15

(iii) 6x + 5 (x - 2) = 6x + 5x -10 = 11x - 10
= 11 x 2 - 10                      [Putting x = -1]
= 22 - 10 = 12

(iv) 4(2x - 1) + 3x + 11 = 8x - 4 + 3x +11 = 8x + 3a - 4 + 11
= 11a + 7 = 11 x 2 + 7 [Putting x = - 1]
= 22+7 = 29

Q7: Simplify these expressions and find their values if x = 3,a = -1, b = - 2 :
(i) 3x - 5 - x + 9
(ii) 2 - 8x + 4x + 4
(iii) 3a + 5 - 8a + 1
(iv) 10 - 3b - 4 - 5b
(v) 2a - 2b - 4 - 5 + a

Ans:
(i) 3a - 5 - x + 9 = 3x - x - 5 + 9 = 2x + 4
= 2x3+4         [Putting a = 3]
= 6 + 4 = 10

(ii) 2 - 8x + 4x + 4 = - 8x + 4x + 2 + 4 = -4x + 6
= - 4 x 3 + 6     [Putting a = 3]
= -12 + 6 =12

(iii) 3a + 5 - 8a + 1 = 3a - 8a + 5 + 1 = - 5a + 6
= -5(- 1) + 6       [Putting a = - 1]
= 5 + 6 = 11

(iv) 10 - 3b - 4 - 5b = - 3b - 5b + 10 - 4 = -8b+6
= -8 (-2)+ 6    [Putting b = -2]
= 16 + 6 = 22

(v) 2a - 2b - 4 - 5 + a = 2a + a - 2b - 4 - 5
= 3a - 2b - 9 = 3 (-1)-2 (-2) -9    [Putting a = -1 , b = - 2]
= -3 + 4 -9 = -8

Q8:
(i) If z = 10, find the value of z3 - 3 (z - 10).
(ii) If p = - 10, find the value of p2 - 2p - 100

Ans:
(i) z3 -3(z-10) = (10)3-3(10 - 10)       [Putting z = 10]
= 1000 - 3 x 0 = 1000- 0
= 1000

(ii) p2 - 2p - 100 = (-10)2 - 2 (-10) - 100    (Putting p = - 10]

= 100+ 20 - 100 = 20

Q9: What should be the value of a if the value of 2x2 + x - a equals to 5, when x = 0 ?
Ans:
Given: 2x2 + x - a = 5
⇒ 2 (0)2 + 0 - a = 5     [Putting x = 0]
⇒ 0 + 0 - a = 5
⇒ a = -5
Hence, the value of a is -5.

Q10: Simplify the expression and find its value when a = 5 and b = - 3: 2 (a2 + ab) + 3 - ab
Ans:
Given: 2 (a2 + ab) + 3 - ab
⇒ 2a2 + 2ab + 3 - ab
⇒ 2a2 + 2ab - ab + 3
⇒ 2a2 + ab + 3
⇒ 2 (5)2 + (5) (-3) + 3   [Putting a = 5 , b = -3]
⇒ 2 x 25 - 15 + 3
⇒ 50 - 15 + 3
⇒ 38

The document NCERT Solutions for Class 8 Maths - Algebraic Expressions- 1 is a part of the Class 7 Course Mathematics (Maths) Class 7.
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## Mathematics (Maths) Class 7

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## FAQs on NCERT Solutions for Class 8 Maths - Algebraic Expressions- 1

 1. What are algebraic expressions?
Ans. Algebraic expressions are mathematical expressions that consist of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. They are used to represent relationships and patterns in mathematics.
 2. How do you simplify algebraic expressions?
Ans. To simplify algebraic expressions, you need to combine like terms by adding or subtracting them. You can also use the distributive property to factor out common factors. Finally, simplify any fractions or exponents present in the expression.
 3. What is the difference between an algebraic expression and an algebraic equation?
Ans. An algebraic expression is a mathematical phrase that contains variables, constants, and operations but does not have an equal sign. An algebraic equation, on the other hand, contains an equal sign and shows the relationship between two algebraic expressions.
 4. How can algebraic expressions be used in real-life situations?
Ans. Algebraic expressions can be used to represent real-life situations such as calculating distances, areas, volumes, and costs. They are also used in science, engineering, and economics to model and solve various problems.
 5. Can you give an example of a complex algebraic expression and how to simplify it?
Ans. An example of a complex algebraic expression could be 3x^2 + 2xy - 5x + 4y^2. To simplify this expression, you would first combine like terms (3x^2 - 5x = 3x^2 - 5x) and then factor out common factors (2xy + 4y^2 = 2y(x + 2y)).

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