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In this page we have Worksheet for Algebraic Expressions and Identities Class 8 Maths Chapter 9 CBSE . Hope you like them and do not forget to like , social share
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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) (a
2+ b
2) (- a
2+ b
2)
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
We will be using below identities in these question
(a + b)² = a² + 2ab + b²
(a – b)² = a² – 2ab + b²
(a – b)(a + b) = a² – b²
a) p² -121
b) 4y² -25
c) 144a²-81
d) 4a²+1/4 -2a
e) 1.21m² -.16
f) b&sup4; -a&sup4;
g) 36x² -49
h) c²/4 - a²/4
i) p²/64 + 9q²/16 +3pq/16 = (p²+36q²+12pq)/64
j) 9a²-81b²
k) 4(a² + 81-18a)
l) 25(x²y²+9z²-6xyz)
m) 36x²+25y²+60xy
n) 36[9p²/4 + 4q²/9 + 2pq]= 9p²+16q² + 64pq
o) x²+.25y²-xy
p) 4x²y²+25y²-20xy²
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) (2a
2+ 9) (2a
2+ 5)
Solution
i) p²+21p+110
ii) 16x² +84x+108
iii) x² -6x+5
iv) 81x²-54x+5
v) 4x² +16xy+15y²
vi) 4a&sup4;+28a² + 45
Question 3
Simplify the following
(i) (x
2- y
2)
2 + 4x
2y
2
(ii) (p + q)
2- (p - q)
2 + p
2q
2
(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 +p
2q
2
(vi) (ab - bc)
2+2ab²c
(vii) (m
2- n
2m)
2+ 2m
2n
2
Solution
i) (x2- y2)2 + 4x2y2= x4+ y4-2x2y2+4x2y2
=x4+ y4+2x2y2=(x2+ y2)2
ii) (p + q)2 - (p - q)2 + p2q2=4pq+p2q2=pq(4+pq)
iii) (2m - 8n)2+ (2m + 8n)2=8m2+128n2
iv) (4m + 5n)2+ (5m + 4n)2 + (4m + 5n) (4m -5n)=16m2+25n2+40mn+25m2+16n2+40mn +16m2-25n2=57m2+16n2+80mn
v) (.5p - 1.5q)2- (.5p - 1.5q)2 +p2q2=3pq+p2q2=pq(3+pq)
vi) (ab - bc)2+2ab²c= a²b²+b²c²-2ab²c+2ab²c=b²(ab²+cb²)
vii) mb&sup4; + nb&sup4;
Question 4
Using identities, evaluate.
a) 91²
b) 89²
c) 202
2
d) 999²
e) 1.2²
f) 397 x 403
g) 48 x 52
h) 5.1
2
i) 61
2- 59
2
j) 11.1
2- 9.9
2
k) 503 x 504
l) 2.1 x 2.2
m) 103 x 98
n) 9.7 x 9.8
o) 729
2- 271
2
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=35
2 -27
2
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 a
2 + 1/a
2
b) If p +q =13 and pq =22, then p
2 + q
2
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
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