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Question
Simplify of the following:
(x+3)3 + (x−3)3
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Solution
In the given problem, we have to simplify equation
Given (x+3)3 + (x−3)3
We shall use the identity `a^3 + b^3 = (a + b)(a^2+b^2 - ab)`
Here `a= (x+3),b= (x-3)`
By applying identity we get
` = (x+ 3+x - 3)[(x+ 3)^2 + (x-3)^2 - (x+ 3)(x-3)]`
` = 2x[(x^2 + 3^2 + 2 xx x xx 3) + (x^2 + 3^2 - 2 xx x xx 3) -(x^2-3^2)]`
` = 2x [(x^2+ 9 + 6x) + (x^2 + 9 - 6 x)-(x^2 - 3^2)]`
` = 2x[x^2 + 9 + 6x + x^2 + 9 -6x - x^2 + 9]`
`= 2x [x^2 + x^2 - x^2 - 6x + 6x+ 9 + 9 + 9]`
` = 2x [x^2 + 27]`
` = 2x^3 + 54x`
Hence simplified form of expression`(x+3)^3 +(x-3)^3`is `2x^3 + 54x`.
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