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Question
The product (a + b) (a − b) (a2 − ab + b2) (a2 + ab + b2) is equal to
Options
a6 + b6
a6 − b6
a3 − b3
a3 + b3
Solution
We have to find the product of `(a+b)(a-b)(a^2 - ab +b^2)(a^2+ab +b^2)`
Using identity
`a^3 +b^3 = (a+b)(a^2 - ab+b^2 )`
`a^3 -b^3 = (a-b)(a^2 +ab+b^2 )`
We can rearrange as
`= (a+b)(a^2 - ab +b^2)(a-b)(a^2 +ab+ b^2)`
`= (a^3 +b^3)(a^3 - b^3)`
Again using the identity `(a+b)(a-b)= a^2 -b^2`
Here `a = a^3,b = b^3`
`(a+b)(a-b) = a^2 - b^2`
` = (a^3)^2 - (b^3)^2`
` = a^6 - b^6`
Hence the product of `(a+b)(a^2 - ab +b^2)(a-b)(a^2+ab +b^2)` is `a^6 - b^6`.
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