Factorise the following: x 6 + 63x 3 - 64

x 6 + 63x 3 - 64 = x 6 + 64x 3 - x 3 - 64 = x 3 (x 3 + 64) - 1(x 3 + 64) = (x 3 + 64)(x 3 - 1) = (x 3 + 4 3 )(x 3 - 1 3 ) We know that, a 3 + b 3 = (a + b)(a 2 + b 2 - ab) a 3 - b 3 = (a - b)(a 2 + b 2 + ab) ∴ (x 3 + 4 3 )(x 3 - 1 3 ) = (x + 4)(x 2 - 4.x + 4 2 )(x - 1)(x 2 + x.1 + 1 2 ) = (x + 4)(x 2 - 4x + 16)(x - 1)(x 2 + x + 1). Hence, x 6 + 63x 3 - 64 = (x + 4)(x 2 - 4x + 16)(x - 1)(x 2 + x + 1).

Mathematics

Factorise the following:
x⁶ + 63x³ - 64

Factorisation

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Answer

x⁶ + 63x³ - 64 = x⁶ + 64x³ - x³ - 64

= x³(x³ + 64) - 1(x³ + 64)

= (x³ + 64)(x³ - 1)

= (x³ + 4³)(x³ - 1³)

We know that,

a³ + b³ = (a + b)(a² + b² - ab)

a³ - b³ = (a - b)(a² + b² + ab)

∴ (x³ + 4³)(x³ - 1³) = (x + 4)(x² - 4.x + 4²)(x - 1)(x² + x.1 + 1²)

= (x + 4)(x² - 4x + 16)(x - 1)(x² + x + 1).

Hence, x⁶ + 63x³ - 64 = (x + 4)(x² - 4x + 16)(x - 1)(x² + x + 1).

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Factorise the following:
x⁶ + 63x³ - 64

Factorisation

Answer

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