Worksheet for Algebraic Expressions and Identities Class 8 Maths Chapter 9 CBSE
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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
(a) 91²=(90+1)²=8100+1+180=8281
(b) 89²=(90-1)²==8100+1-180=7921
(c) 2022=(200+2)2=40000+4+800=40804
(d) 999²=(1000-1)²=1000000+1 -2000=998001
(e) 1.2²=(1+.2)²=1+.04+.4=1.44
(f) 397 x 403=(400-3)(400+3)=160000-9=159991
(g) 48 x 52=(50-2)(50+2)=2500-4=2496
(h) 5.12=(5+.1)2=25+.01+1=26.01
(i) 612- 592=(61-59)(61+59)=2*120=240
(j) 11.12- 9.92=(11.1-9.9)(11.1+9.9)=1.2*21=25.2
(k) 503 x 504=(500+3)(500+4)=250000+12+3500=253512
(l) 2.1 x 2.2=(2+.1)(2+.2)=4+.6+.02=4.62
(m) 103 x 98=(100+3)(100-2)=10000-6+100=10094
(n) 9.7 x 9.8=(10-.3)(10-.2)=100+.06-5=95.06
(o) 7292- 2712=(729-271)(729+271)=458*1000=458000
Question 5
Find the value of x if 8x=352 -272 Solution
8x=352 -272
8x=(35-27)(35+27)
8x=8*62
x=62
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
(a) a- 1/a=4
Squaring both the sides
a2 + 1/a2-2=16
a2 + 1/a2=18
(b) p2 + q2=(p+q)2 -2pq
=132-2*22=169-44=125
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
(i) False as the terms are same and it is equal to 3abc
(ii) False
(iii) false
(iv) True
(v) false
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
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.