Question

Factorise , x(x-y)^3+3x^2y(x-y)​

Answer 1

ANSWER✔

$\sf\dashrightarrow x(x-y)^3+3x^2y(x-y)$

✯.USING IDENTITY,

$\large{\boxed{\bf{\star\:\: a^2-b^2=(a-b)(a^2+ab+b^2)= (a-b)^3+3ab(a-b) \:\: \star }}}$

$\sf\implies x(x-y)^3+3x^2y(x-y)$

$\sf\implies x(x-y)(x^2+xy+y^2)$

$\sf\implies x^4-xy^3=x(x-y)(x^2+xy+y^2) \:---[from\:given\:identity]$

$\sf\implies x(x-y)(x^2+xy+y^2)$

$\large{\boxed{\bf{\star\:\: x(x-y)(x^2+xy+y^2) \:\: \star }}}$

________________

Answer 2

$\large\underline{\underline{\bold{\pink{\mathfrak{AnSwEr}}}}}$ANSWER✔

$\sf\dashrightarrow x(x-y)^3+3x^2y(x-y)$

USING IDENTITY,

$\rm{\boxed{\bf{\star\:\: a^2-b^2=(a-b)(a^2+ab+b^2)= (a-b)^3+3ab(a-b) \:\: \star }}}$

$\sf\implies x(x-y)^3+3x^2y(x-y)$

$\sf\implies x(x-y)(x^2+xy+y^2)$

$\sf\implies x^4-xy^3=x(x-y)(x^2+xy+y^2) \:---[from\:given\:identity]$

$\sf\implies x(x-y)(x^2+xy+y^2)$

$\large{\boxed{\bf{\star\:\: x(x-y)(x^2+xy+y^2) \:\: \star }}}$