Question

Factorise 8 x cube minus 64

Answer 1

 

Factor 8x^3-64

8x3−648x3-64

Factor 88 out of 8x3−648x3-64.

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8(x3−8)8(x3-8)

Rewrite 88 as 2323.

8(x3−23)8(x3-23)

Since both terms are perfect cubes, factor using the difference of cubes formula, a3−b3=(a−b)(a2+ab+b2)a3-b3=(a-b)(a2+ab+b2) where a=xa=x and b=2b=2.

8((x−2)(x2+x⋅2+22))8((x-2)(x2+x⋅2+22))

Factor.

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8(x−2)(x2+2x+4)8(x-2)(x2+2x+4)