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(i) (2x + 5y)
3
(ii) (5p – 3q)
3
(iii) (-a + 2b)
3
(i)
Using the identity
(x + y)
3
= x
3
+ 3x
2
y + 3xy
2
+ y
3
we get
(2x + 5y)
3
= (2x)
3
+ 3(2x)
2
(5y) + 3(2x)(5y)
2
+ (5y)
3
= 8x
3
+ 60x
2
y + 150xy
2
+ 25y
3
(ii)
Using the identity
(x - y)
3
= x
3
- 3x
2
y + 3xy
2
- y
3
we get
(5p - 3q)
3
= (5p)
3
-3(5p)
2
(3q)+3(5p)(3q)
2
-(3q)
3
= 125p
3
- 225p
2
q + 135pq
2
- 27q
3
(iii)
Using the identity for
(x + y)
3
we get
(-a + 2b)
3
= (-a)
3
+3(-a)
2
(2b)+3(-a)(2b)
2
+(2b)
3
= a
3
+ 6a
2
b - 12ab
2
+ 8b
3
20