Factorise the following 3ab² - 12a²b
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Answered by
1
We solve the given expression a
3
+3a
2
b+3ab
2
+b
3
−8 as shown below:
a
3
+3a
2
b+3ab
2
+b
3
−8
=(a+b)
3
−(2)
3
(∵(x+y)
3
=x
3
+y
3
+3x
2
y+3xy
2
)
=(a+b−2)[(a+b)
2
+2
2
+2(a+b)](∵x
3
−y
3
=(x−y)(x
2
+y
2
+xy))
=(a+b−2)(a
2
+b
2
+2ab+4+2a+2b)(∵(x+y)
2
=x
2
+y
2
+xy)
Hence, a
3
+3a
2
b+3ab
2
+b
3
−8=(a+b−2)(a
2
+b
2
+2ab+4+2a+2b)
Answered by
0
Answer:
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