Question

factorise x6 + 729. 6 is the power of x

Answer 1

$Factorising\ by\ the\ formula:\ a^3 + b^3 = (a + b)(a^2 - 2ab + b^2) \\ \\ \\ x^6 + 729 \\ \\ = x^{2 \times 3} + 9^3 \\ \\ = (x^2)^3 + 9^3 \\ \\ \\ \therefore\ a = x^2;\ b = 9 \\ \\ \\ \therefore\ (x^2)^3 + 9^3 = (x^2 + 9)((x^2)^2 - (x^2 \times 9) + 9^2) \\ \\ = x^6 + 729 = (x^2 + 9)(x^4 - 9x^2 + 81)$

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