The correct option is A (x+4)(x^2 4x+16) x^3+64=x^3+4^3 #160;We know that the sum of two cubes, x^3+y^3= (x+y)(x^2 xy+y^2) So, x^3+4^3 = ...

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(a + b)^2 Expansion and Visualisation

Factorise: ...

Question

Factorise: $x^{3} + 64$

(x + 4) (x^{2} - 4 x + 16)

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(x - 4) (x^{2} - 4 x + 16)

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(x + 4) (x^{2} + 4 x + 16)

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(x - 4) (x^{2} - 4 x - 16)

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Solution

The correct option is A $(x + 4) (x^{2} - 4 x + 16)$
$x^{3} + 64 = x^{3} + 4^{3}$
We know that the sum of two cubes, $x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})$
So, $x^{3} + 4^{3} = (x + 4) (x^{2} - 4 x + 4^{2})$
$x^{3} + 4^{3} = (x + 4) (x^{2} - 4 x + 16)$

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