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Factorize: a^3+3a^2b+3a b^2+b^3-8...

Factorize: `a^3+3a^2b+3a b^2+b^3-8`

Text Solution

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Given expression
`a^3+3a2^b+3ab^2+b^3−8`
`(a+b)^3−(2)^3`
`(∵(x+y)^3=x^3 +y^3+3x^2y+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)`.
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