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Class 8 Maths - Algebraic Expressions and Identities CBSE Worksheets Solutions

Fill in the blanks

Q1: Terms with the same algebraic factors are called ____________ terms.
Ans:
Like

Q2: A ________________ can take any value and ________________ has a fixed value.
Ans:
Variable, constant 

Q3: An expression with one or more terms is called _____________
Ans
: Polynomial

Q4: An expression with one term is called __________________ with two terms is ______________ and with three terms is _______________
Ans
: Monomial, binomial, trinomial 

Q5: An algebraic expression with equality sign is called ______________
Ans
: Equation 

State True or False

Q1: The degree of a constant term is 0
Ans:
True

Q2: The difference between two like terms is a like term.
Ans: 
True

Q3: 1 is an algebraic expression
Ans:
True

Q4: The expression x + y + 5x is a trinomial.
Ans
: False

Q5: In like terms, the numerical coefficients should also be the same
Ans:
False

Answer the following questions

Q1: The volume of a rectangular box where length, breadth, and height are 2a,4b,8crespectively.
Ans:
Given: length of a rectangular box, l=2a
Breadth of rectangular box, b=4b
Height of rectangular box, h=8c
We need to find the volume of the rectangular box with the given dimensions.
We know the volume of a cuboid =l×b×h
Therefore, the volume of the rectangular box will be
=2a×4b×8c=64abc

Q2: Simplify (p+q2)(p2−q)
Ans:
Given: (p+q2)(p2−q)
We need to simplify the given expression.
To simplify, we will open the brackets by multiplying the terms in it with each other.
Therefore, the expression will become
(p+q2)(p2−q)

=p(p2−q)+q2(p2−q)

=p3−pq+q2p2−q3

Q3: If pq=3 and p+q=6, then (p2+q2) is
Ans:
Given: pq=3
, p+q=6,
We need to find (p2+q2)
We know that,
(p+q)2=p2+q2+2pq

(p2+q2)=(p+q)2−2pq
Substituting the values, pq=3
, p+q=6,
in above equation we get
(p2+q2)=(6)2−2(3)=36−6=30

Q4: Simplify x(2x−1)+5 and find its value at x=−3
Ans:
Given: x(2x−1)+5
We need to find the value of the given expression at x=−3
We will substitute x=−3 in the given expression. 

Therefore, the expression after simplifying will be
2(−3)2−(−3)+5

=2(9)+3+5

=18+8

=26

Q5: Simplify the expression and evaluate them as directed:  2x(x + 5) - 3(x - 4) + 7 for x = 2

Ans: Simplify 2x(x + 5) - 3(x - 4) + 7:

= 2x2 + 10x - 3x + 12 + 7
= 2x2 + 7x + 19
For x = 2 :
2(2)2 + 7(2) + 19 
= 2(4) + 14 + 19
= 8 + 14 + 19 = 41

Q6: Think of a number x. Multiply it by 3 and add 5 to the product and subtract y subsequently. Find the resulting number.

Ans: Required number is (3x + 5)
Now we have to subtract y from the result i.e., 3x + 5 – y

Q7: From the sum of 3a−b+9 and −b−9, subtract 3a−b−9
Ans:
Given: expressions 3a−b+9, −b−9, 3a−b−9
We need to subtract 3a−b−9
from the sum of 3a−b+9
and −b−9
The sum of the first two terms, −b−9
and 3a−b+9
will be
3a−b+9+(−b−9)=3a−b+9−b−9=3a−2b
Now subtracting 3a−b+9
from 3a−2b
, we get
3a−2b−(3a−b−9)=3a−2b−3a+b+9=−b+9

Q8: Simplify the expression and evaluate them as directed:4y(3y - 2) + 5(y + 3) - 12fory = -1

Ans: Simplify 4y(3y - 2) + 5(y + 3) - 12

= 12y2 - 8y + 5y + 15 - 12
= 12y2 - 3y + 3
For y = -1:
12(-1)2 - 3(-1) + 3
= 12(1) + 3 + 3
= 12 + 3 + 3 = 18

Q9:Add 4x(2x + 3) and 5x2 - 7x + 10.

Ans: 
1. Expand 4x(2x + 3):
4x(2x + 3) = 8x2 + 12x
2. Add 8x2 + 12x to 5x2- 7x + 10:
(8x2 + 12x) + (5x2 - 7x + 10)
3. Combine like terms:
8x2 + 5x2 + 12x - 7x + 10 = 13x2 + 5x + 10
The result is 13x2 + 5x + 10.

Q10: Simplify (x2−3x+2)(5x−2)−(3x2+4x−5)(2x−1)
Ans:Given: (x2−3x+2) (5x−2) − (3x2+4x−5) (2x−1)
We need to simplify the given expression.
First simplifying, (x2−3x+2) (5x−2),
we will get
(x2−3x+2)(5x−2)

=5x3−15x2+10x−2x2+6x−4

=5x3−17x2+16x−4 ...................(1)
Now simplifying, (3x2+4x−5)(2x−1), we will get
(3x2+4x−5)(2x−1)

=6x3+8x2−10x−3x2−4x+5

=6x3+5x2−14x+5 ..................(2)
Subtract (1)−(2) to get the result
(x2−3x+2)(5x−2)−(3x2+4x−5)(2x−1)

=5x3−17x2+16x−4−[6x3+5x2−14x+5]

=5x3−17x2+16x−4−6x3−5x2+14x−5

=−x3−22x2+30x−9

The document Class 8 Maths - Algebraic Expressions and Identities CBSE Worksheets Solutions is a part of the Class 8 Course Mathematics (Maths) Class 8.
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FAQs on Class 8 Maths - Algebraic Expressions and Identities CBSE Worksheets Solutions

1. What are algebraic expressions?
Ans.Algebraic expressions are mathematical phrases that can include numbers, variables (like x or y), and operations (such as addition, subtraction, multiplication, and division). They do not contain equal signs and can represent a wide variety of values depending on the variables involved.
2. How do you simplify an algebraic expression?
Ans.To simplify an algebraic expression, combine like terms (terms that have the same variable raised to the same power) and perform any arithmetic operations. For example, in the expression 3x + 2x - 5, you would combine 3x and 2x to get 5x, resulting in 5x - 5.
3. What are algebraic identities?
Ans.Algebraic identities are equations that are true for all values of the variables involved. Common examples include the identity (a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b². These identities help in simplifying expressions and solving equations.
4. How do you use algebraic identities to factor expressions?
Ans.Algebraic identities can be used to factor expressions by recognizing patterns in the expression that match the identities. For example, to factor x² - 9, you can recognize it as a difference of squares and use the identity a² - b² = (a + b)(a - b), resulting in (x + 3)(x - 3).
5. Why are algebraic expressions and identities important in mathematics?
Ans.Algebraic expressions and identities are important because they form the foundation for solving equations and understanding mathematical relationships. They are used in various fields, including science, engineering, and economics, to model situations and solve real-world problems.
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