Worksheet for Algebraic Expressions and Identities Class 8 Maths Chapter 9 CBSE

Short answer type

Question 1
Use a suitable identity to get each of the following products.
(a) (p - 11) (p + 11)
(b) (2y + 5) (2y - 5)
(c) (12a - 9) (12a +9)
(d) (2a-1/2)(2a-1/2)
(e) (1.1m - 0.4) (1.1m + 0.4)
(f) (a²+ b²) (- a²+ b²)
(g) (6x - 7) (6x + 7)
(h) (- a/2 + c/2) (- a/2 + c/2)
(i) [(p/8)+(3q/4)] [(p/8)+(3q/4)]
(j) (3a + 9b) (3a - 9b)
(k) 2(a - 9)²
(l) 5(xy - 3z)²
(m) (6x+ 5y)²
(n) 36[(3p/2}) + (2q/3)]²
(o) (x - 0.5y)²
(p) (2xy - 5y)²
Solution
Question 2
Use the identity (x + a) (x + b) = x^2 + (a + b) x + ab to find the following products.
(i) (p + 10) (p + 11)
(ii) (4x + 9) (4x + 12)
(iii) (x - 5) (x - 1)
(iv) (9x - 5) (9x - 1)
(v) (2x + 5y) (2x + 3y)
(vi) (2a²+ 9) (2a²+ 5)
Solution
Question 3
Simplify the following
(i) (x²- y²)² + 4x²y²
(ii) (p + q)²- (p - q)² + p²q²
(iii) (2m - 8n)²+ (2m + 8n)²
(iv) (4m + 5n)²+ (5m + 4n)² + (4m + 5n) (4m -5n)
(v) (.5p - 1.5q)²- (.5p - 1.5q)² +p²q²
(vi) (ab - bc)²+2ab²c
(vii) (m²- n²m)²+ 2m²n²
Solution

Question 4
Using identities, evaluate.
(a) 91²
(b) 89²
(c) 202²
(d) 999²
(e) 1.2²
(f) 397 x 403
(g) 48 x 52
(h) 5.1²
(i) 61²- 59²
(j) 11.1²- 9.9²
(k) 503 x 504
(l) 2.1 x 2.2
(m) 103 x 98
(n) 9.7 x 9.8
(o) 729²- 271²
Solution
Question 5
Find the value of x if 8x=35² -27²
Solution
Question 6
(a) If a -1/a =4, find the value of a² + 1/a²
(b) If p +q =13 and pq =22, then p² + q²
Solution

True and False

Question 7
(i) abc + bca + cab is a monomial.
(ii) An equation is true for all values of its variables.
(iii) $(a - b)^2 = a^2 - b^2$
(iv) a ( b + c) = ab + ac is a distributive Property
(v) $(a + b)^2 - (a - b)^2 = 2a^2 - 2b^2$
Solution

Fill in the blanks

Question 8
(i) $(a -2b))(a+ 2b)(a^2 + 4b^2)$ is _________
(ii) (a - b)²2 + ____________ = a² - b²
(iii) The coefficient in -7abc is _____
(iv)If a+b=9 and ab=14, the $a^2 + b^2$ is ______
(v) $82^2 -18^2$ is _____
Solution

Multiple Choice questions

Question 9
if $a^2 + b^2=74$ and $a+b=12$,then the value of ab is
(a) 35
(b) 32
(c) 40
(d) 37
Question 10
In a polynomial, the exponents of the variables are always
(a) integers
(b) positive integers
(c) non-negative integers
(d) non-positive integers
Question 11
if $x + \frac {1}{x}=4$ then the value $x - \frac {1}{x}$ is
(a) 16
(b) 4
(c) $\sqrt {12}$
(d) 0
Question 12
$(x^4 +1)(x^2 +1)(x+1)(x-1)$ is
(a) $x^4 -1$
(b) $x^4 +1$
(c) $x^{8} -1$
(d) $x^{16} -1$
Question 13
$x + \frac {1}{x}=5$ then $x^3 + \frac {1}{x^3}$ is
(a) 110
(b) 100
(c) 625
(d) 125
Solution

Match the column

Question 14

Solution

Summary

This algebraic expressions and identities class 8 worksheets with solutions is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail.

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