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Question
Factorize the following expressions:
( x + 2)3 + ( x - 2)3
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Solution
`= (x + 2 + x - 2)((x + 2^2 -(x + 2)(x - 2) + (x - 2)^2) [∵ a^3 + b^3 = (a + b)(a^2 - ab + b^2)]`
`= 2x(x^2 + 4x + 4 - (x + 2)(x - 2) + x^2 - 4x + 4) [∵ (a + b)^2 = a^2 + 2ab + b^2, (a - b)^2 = a^2 - 2ab + b^2]`
`= 2x (2x^2 + 8 - (x^2 - 2^2))` `[∵ (a + b)(a - b) = a^2 - b^2]`
`=2x(2x^2 + 8 - x^2 + 4)`
`= 2x(x^2 + 12)`
`∴ (x + 2)^3 + (x - 2)^3 = 2x(x^2 + 12)`
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