Let us factorise the following algebraic expressions:
(x² – x) y² + y – (x² + x)

Question

Let us factorise the following algebraic expressions:(x2 – x) y2 + y – (x2 + x)

Philoid · Accepted Answer

The given expression can be rewritten as:

x(x – 1)y² + x²y – (x² – 1)y – x(x+1)

⇒ x² – xy² + x²y – x²y + y – x² – x

As we know that a² – b² = (a + b)(a – b)

⇒ xy[(x – 1)y + x] – (x + 1)[(x – 1)y + x]

⇒ (xy – x - 1)(xy + x – y)