Question

Factories.
$(x + 1)^{4} - (x - 1) ^{4}$

Answer 1

Heya user☺☺

It can be written as

(x^2 + 1 + 2x)^2 - (x^2 +1 - 2x)^2

Using identity of a^2 - b^2 = (a+b)(a-b), we have

( x^2 + 1 + 2x + x^2 +1 - 2x)( x^2 + 1 + 2x - x^2 - 1 + 2x)

(2x^2 + 2)(4x)

4(x^2 + 1)(2x)

8(x^2 + 1)(x)

Hope this will help you☺☺

Answer 2

Hey here is your answer
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$= (x + 1)^{4} - (x - 1) ^{4} \\ \\ = {( {(x + 1)}^{2}) }^{2} - {( {(x - 1)}^{2}) }^{2} \\ \\ = ({(x + 1)}^{2} + {(x - 1)}^{2}).({(x + 1)}^{2} - {(x - 1)}^{2}) \\ \\ = ( {x}^{2} + 1 + 2x + {x}^{2} + 1 - 2x).((x + 1 + x - 1)(x + 1 - x + 1)) \\ \\ = (2 {x}^{2} + 2).((2x)(2)) \\ \\ = (2 {x}^{2} + 2).(4x) \\ \\ = 8 {x}^{3} + 8x \\ \\ = 8x( {x}^{2} + 1)$
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Hope it may helpful to you
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