Question

The Difference of Square: a^2 - b^2 = (a + b)(a - b)


Sara did a question as: 2x^2 - 2y^2 = (2x + 2y)(2x - 2y).


What's wrong with Sara's work? How to fix it?

Answer 1

Answer:

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

Step-by-step explanation:

Given

Difference of two squares: $a^2 - b^2 = (a + b)(a - b)$

Sara Solution to a question: $2x^2 - 2y^2 = (2x + 2y)(2x - 2y).$

Required

State what's wrong with Sara's work

How to fix it

In Sara's solution, the coefficient of x and y is 2. Sara's solution is wrong because she included the coefficients of x and y when converting the expression to difference of two squares.

To fix this, the very first thing that needs to done is to factorize the given expression (as follows)

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

Then the difference of two squares can be applied on the expression in bracket. This gives

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