Question

solve this
$x \: \: - \ 3 \\ 3 \: \: \: \: \: \: \: \: x$
expand formula
$(a - b) {}^{3 } = \: a {}^{3} - 3a {}^{2}b \: + 3ab {}^{2} - \: b {}^{3}$

Answer 1

$L. \: H. \: S .\: = (a - b) {}^{3} \\ \\ = (a - b)(a - b) {}^{2} \\ \\ = (a - b)(a {}^{2} - 2ab + b {}^{2} ) \\ \\ = a(a {}^{2} - 2ab + b {}^{2} ) - b(a {}^{2} - 2ab + b {}^{2} ) \\ \\ = a {}^{3} - 2a {}^{2} b + ab {}^{2} - a {}^{2} b + 2ab {}^{2} - b {}^{3} \\ \\ = a {}^{3} - 2a {}^{2} b - a {}^{2} b + ab {}^{2} + 2ab {}^{2} - b {}^{3} \\ \\ = a {}^{3} - 3a {}^{2} b + 3ab {}^{2} - b {}^{3} \\ \\= R .\: H .\: S \: .$



$(x - 3){}^{3} \\ \\ = x{}^{3}-3×(x){}^{2}×3+3×x×(3){}^{2}-3{}^{3} \\ \\ = x{}^{3}-9x{}^{2}+27x-27$