Question

(X-3)^3 expand in cubes

Answer 1

$\implies {(x - 3)}^{3}$

we know that :-

${(a-b)^3 = a^3 - b^3 - 3ab(a-b)}$

$\implies {(x - 3)}^{3} = {(x)}^{3} - {(3)}^{3} - 3.3.x(x - 3)$

$\implies{(x)}^{3} - 27 - 9x(x - 3)$

$\implies{x}^{3} - 27 - 9 {x}^{2} + 27x$

$\implies{x}^{3} - 9 {x}^{2} + 27x- 27$

Answer :

$\implies{x}^{3} - 9 {x}^{2} + 27x- 27$

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Attach as Additional Information:-

$\implies{(a+b)^2 = a^2 + b^2 + 2ab}$

$\implies{(a-b)^2 = a^2 + b^2 - 2ab}$

$\implies{(a+b)^3 = a^3 + b^3 + 3ab(a + b)}$

$\implies{(a-b)^3 = a^3 - b^3 - 3ab(a-b)}$

$\implies{(a^3+b^3)= (a+b)(a^2 - ab + b^2)}$

$\implies{(a^3-b^3)= (a-b)(a^2 + ab + b^2)}$

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Also :-

$1)a^m \times a^n= {a}^{(m + n)}$

$2) {( {a}^{m})}^{n}  = {a}^{mn}$

$3) {ab}^{n} = {a}^{n} {b}^{n}$

$4) \frac{ {(a)}^{m} }{ {(a)}^{n} } = {a}^{m - n}$

$5) {a}^{ - b} = \frac{1}{ {a}^{b} }$