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:

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

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