Question

Factorise x(x+z) -y(y+z)
Show calculation and please give correct answers.​

Answer 1

Answer:

(x-y)(x+y+z)

Step-by-step explanation:

$x^{2} +xz-y^{2} -yz\\x^{2} -y^{2} +z(x-y)\\(x+y)(x-y)+z(x-y)\\(x-y)(x+y+z)$

Answer 2

Answer:

(x - y)(x + y + z)

Step-by-step explanation:

Given

x(x + z) - y(y + z) ← distribute both parenthesis

= x² + xz - y² - yz ← rearrange

= x² - y² + xz - yz ← x² - y² can be factored as a difference of squares

= (x - y)(x + y) + z(x - y) ← factor out (x - y) from each term

=(x - y)(x + y + z)