Question

a³-14ab²+7a²b-8b³ пж
​

Answer 1

a³ - 14ab² + 7a²b - 8b³ = (a³ - 8b³) - (14ab² - 7a²b) = [a³ - (2b)³] - 7ab(2b -a) =

= (a - 2b)(a² + 2ab + 4b²) + 7ab(a - 2b) = (a - 2b)( a² + 2ab + 4b² + 7ab) =

= (a - 2b)(a² + 9ab + 4b²)

Answer 2

$a^{3}-14ab^{2}+7a^{2} b-8b^{3}=(a^{3}-8b^{3})+(7a^{2}b-14ab^{2})=\\\\=[a^{3}-(2b)^{3}] +7ab(a-2b)=(a-2b)( a^{2}+2ab+4b^{2})+7ab(a-2b)=\\\\=(a-2b)(a^{2}+2ab+4b^{2}+7ab)=\boxed{(a-2b)(a^{2}+9ab+4b^{2})}$