Question

factorize x(x+y)³ -3x²y(x+y)​

Answer 1

Here is your answer

hope it helps

Answer 2

Factors are

$\bf \red{x {(x + y)}^{3} - 3 {x}^{2} y(x + y) = x(x + y)( {x}^{2} + {y}^{2} - xy) }$

Given:

• $x {(x + y)}^{3} - 3 {x}^{2} y(x + y)$

To find:

• Find the factors of polynomial.

Solution:

Step 1:

Analyse the polynomial and search for any common factor in first go.

$\red{x (x + y)}{(x + y)}^{2} - 3 {x} y \red{x(x + y)}$

it is clear that x(x+y) is common.

$x {(x + y)}^{3} - 3 {x}^{2} y(x + y) \\ = x(x + y)( {(x + y})^{2} - 3xy)$

Step 2:

Apply identity

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

So,

$x {(x + y)}^{3} - 3 {x}^{2} y(x + y) \\ = x(x + y)( {x}^{2} + {y}^{2} + 2xy - 3xy)$

or

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

Thus,

Factors are

$\bf \: x {(x + y)}^{3} - 3 {x}^{2} y(x + y) = x(x + y)( {x}^{2} + {y}^{2} - xy)$

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