Question

Factorise :
- (x - y)² – (x - y)².​

Answer 1

Step-by-step explanation:

(x+y)² - (x-1)²= (x²+y²+2xy)-(x²+y²-2xy)= x²+y²+2xy-x²-y ..process.

expand your brackets. You should get the following; 2x^2 -4xy +2y^2.

This is a quadratic expression, and there are a number of ways to factorise a quadratic expression. The one I’m going to use, is called the grouping method. Using that, I get the following; 2x^2 -2xy -2xy +2y^2.

I will group the first two terms together, and the last two terms together, and I get the following; 2x(x-y) -2y(x-y).

Thereafter, to simplify it, I get the following; (2x-2y) (x-y).

I can simplify it further, (by factoring out a 2 from the 1st parentheses) and I get the following; 2 (x - y) (x - y).

Finally (the answer), to simplify it completely, I get the following; 2 (x - y)^2