Question

x
${x}^{3} + {y}^{3 } - 12xy + 64$
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Answer 1

Answer:

$(x {}^{3} + y {}^{3} - 12xy + 64) \\ (x {}^{3} + y {}^{3} + 4 {}^{3} - 12xy) \\ (x + y + 4)(x {}^{2} + y {}^{2} + 4 {}^{2} - xy - 4y - 4x) \\ (x + y + 4)(x {}^{2} + y {}^{2} + 16 - xy - 4y - 4x) \\ = (x + y + 4) \\ (x {}^{2} + y {}^{2} + 16 - xy - 4y - 4x)$

USING THE IDENTITY

$(a {}^{3} + b {}^{3} + c {}^{3} - 3abc) \\ = (a + b + c)(a {}^{2} + b {}^{2} + c {}^{2} - ab - bc - \\ - ca)$