Question

4. Factorize x (x - 1) - y(y - 1).

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Answer 1

x(x-1)-y(y-1)

= x²-x-y²+y

= (x²-y²)-(x-y)

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

= (x-y)(x+y+1)

Answer 2

$x(x-1)-y(y-1)=(x-y)(x+y-1)$

Step-by-step explanation:

Given : Expression $x(x-1)-y(y-1)$

To find : Factorize the expression ?

Solution :

Expression $x(x-1)-y(y-1)$

Solve by distributive property, $a(b+c)=ab+ac$

$x(x-1)-y(y-1)=x^2-x-y^2+y$

Apply commutative property, $a+b=b+a$

$x(x-1)-y(y-1)=x^2-y^2-x+y$

$x(x-1)-y(y-1)=(x^2-y^2)-(x-y)$

Apply identity, $a^2-b^2=(a+b)(a-b)$

$x(x-1)-y(y-1)=(x+y)(x-y)-(x-y)$

$x(x-1)-y(y-1)=(x-y)(x+y-1)$

Therefore, the factorization is $x(x-1)-y(y-1)=(x-y)(x+y-1)$

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