Question

Factorise 1+64x^3 plz help me

Answer 1

$\begin{array}{|r|l|}\cline{1-2}&\\\textbf{Given:}&1+64x^3\\&\\\cline{1-2}&\\\textbf{To find:}&\text{Factors of 1+64x^3 }\\&\\\cline{1-2}&\\\textbf{Solution:}&\\&\text{Consider}\\&\\&1+64x^3\\&\\&=1^3+4^3x^3\\&\\&=1^3+(4x)^3\\&\\&\text{Using the identity}\\&\boxed{\bf\,a^3+b^3=(a+b)(a^2-ab+b^2)}\\&\\&=(1+4x)(1^2-4x+(4x)^2)\\&\\&=(1+4x)(1-4x+16x^2)\\&\\&\\\cline{1-2}&\\\textbf{Answer:}&\textbf{Factors of 1+64x^3 are (1+4x) and (1-4x+16x^2) }\\&\\\cline{1-2}\end{array}$

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