Worksheet Solutions: We Distribute, Yet Things Multiply | Worksheets with Solutions for Class 8 PDF Download

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

Explanation: Like terms have the same variables raised to the same powers (e.g., 3x and 5x).

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

Explanation: A variable changes (e.g., x), a constant stays the same (e.g., 5).

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

Explanation: An algebraic expression is a combination of variables and constants.

Examples:

• 2x+3 → algebraic expression

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

Explanation:

• 1 term = monomial (e.g., 4x)

• 2 terms = binomial (e.g., x + y)

• 3 terms = trinomial (e.g., x² + 2x + 3)

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

Explanation: An equation has an equals (=) sign between two expressions.

State True or False

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

Explanation: A constant term (like 3, −7, or 100) has no variable.
It can be written as: 3 = 3 × x⁰

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

Explanation: Like terms have the same variables and powers.
For example: 6x and 4x are like terms.

• Their difference: 6x − 4x = 2x

Q3: 1 is an algebraic expression
Ans: True

Explanation:
An algebraic expression can include: constants, variables, or both.
The number 1 is a constant, so it's a valid algebraic expression.

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

Explanation: Before deciding the number of terms, we must combine like terms.
Here, x and 5x are like terms.
x + y + 5x = 6x + y → Only 2 terms 
→ It's a binomial, not a trinomial.

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

Explanation: Like terms need to have the same variables with the same powers, but the coefficients can be different.

For example: 2xy and 7xy are like terms (same variables, different coefficients)

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
=2a × 4b × 8c
=64abc
Q2: Carry out the multiplication of the expressions in each of the following pairs.
(i) ​​​​p − q, 9pq²
(ii) b² − 16, 5b

Ans: (i) (p − q) × 9pq²

We multiply each term of the bracket (p and −q) with 9pq²:
= p × 9pq² − q × 9pq²
= 9p²q² − 9pq³

(ii) (b² − 16) × 5b

Multiply each term in the bracket by 5b:
= b² × 5b − 16 × 5b
= 5b³ − 80b

Q3: 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
Q4: 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
Q5: Add: x(x − y), y(y − z), and z(z − x)
Ans: x(x − y) + y(y − z) + z(z − x)
First expand each expression:
1. x(x−y)=x²−xy
2. y(y−z)=y²−yz
3. z(z−x)=z²−zx

Add all the expressions: 
x² − xy + y²− yz +z² − zx
Rearrange like terms:
x²+ y²+ z²- xy -yz -zx

Q6: Multiply: (m² + 3n²) × (2m − n)

Sol: (m² + 3n²) × (2m − n)
= m² × (2m − n) + 3n² × (2m − n)
= 2m³ − m²n + 6mn² − 3n³

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) - 12for y = -1

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

Q9:Add 4x(2x + 3) and 5x² - 7x + 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