Question

Factor the expression below.

49a2 – 25b2

Which of the following binomials is a factor of the expression?

Answer 1

(7a+5b)(7a-5b) is correct

Answer 2

`49a^(2) - 25b^(2) = (7a + 5b)(7a - 5b)`

Explanation:

The most common factorization of binomial expressions are:

`(x + y)^(2) = x^(2) + 2xy + y^(2)`

`(x - y)^(2) = x^(2) - 2xy + y^(2)`

`(x + y)*(x - y) = x^(2) - y^(2)`

This goes both ways, that is,
`(x + y)*(x - y) = x^(2) - y^(2)`, just as,
`x^(2) - y^(2) = [tex](x + y)*(x - y)`

So

`49a^(2) - 25b^(2) = (7a + 5b)(7a - 5b)`