Question

factorise x(x+y)^3-3x^2y(x+y)​

Answer 1

Answer:

x×(x+y) × (x² + 2xy + y ²-3x)

Step-by-step explanation:

Factor out x×(x + y) from the expression

x×(x + y) ×((x + y)² - 3x)

Use (a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2 to expand the expression

x×(x+y) × (x² + 2xy + y ²-3x)

Answer 2

Answer:

After factoring the expression becomes

$x(x+y)^3-3x^2y(x+y)=x(x+y)(x^2+y^2-xy)$.

Step-by-step explanation:

Given expression is $x(x+y)^3-3x^2y(x+y)$.

We need to factorize the given expression.

Factorization or factoring consists of writing a number or another mathematical object as a product of several factors.

Taking $x(x+y)$ as common from the expression,

$x(x+y)((x+y)^2-3xy)$

Use the formula $(x+y)^2=x^2+y^2+2xy$

Expanding the $(x+y)^2$ term using the formula,

$x(x+y)(x^2+y^2+2xy-3xy)$

Now subtracting the coefficients of similar terms,

$x(x+y)(x^2+y^2-xy)$

After factoring, the expression becomes

$x(x+y)^3-3x^2y(x+y)=x(x+y)(x^2+y^2-xy)$.