(A) We have,$1+64 x^{3} = (1)^{3} + (4 x)^{3}$Using the algebraic identity $a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})$,where $a = 1$ and $b = 4x$:$=

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(A) We have,$1+64 x^{3} = (1)^{3} + (4 x)^{3}$Using the algebraic identity $a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})$,where $a = 1$ and $b = 4x$:$= (1 + 4x)((1)^{2} - (1)(4x) + (4x)^{2})$$= (1 + 4x)(1 - 4x + 16x^{2})$$= (1 + 4x)(16x^{2} - 4x + 1)$