Question

factorise -8a³+36a²-54a+27​

Answer 1

$\huge{\mathbb{\red{ANSWER:-}}}$

$\sf{-8a^3 + 36a^2 - 54a + 27}$

$-(\sf{8a^3 - 36a^2 + 54a - 27})$

$-(\sf{8a^3 - 27 - 36a^2 + 54a})$

$-(\sf{(2a)^3 - (3)^3 - 18a(2a - 3)})$

$-[\sf{(2a)^3 - (3)^3 - 3(6a)(2a - 3)}]$

$-[\sf{(2a)^3 - (3)^3 - 3(2a)(3)(2a - 3)}]$

We Know that -

$\small\boxed{\sf{a^3 - b^3 - 3ab(a - b)=(a - b)^3}}$

So ,

$-(2a - 3)^3$

other important algebraic formulas:-

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

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

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

(4)$\sf{(a^2 - b^2) =(a + b)(a - b)}$

(5)$\sf{if \: (a + b + c) = 0}$

$\sf{then, \: (a^3+b^3+c^3)=3abc}$