Question

How do you recognize if a binomial is a difference of perfect squares and how is the pattern used to factor the binomial?

Answer 1

Explanation:

An example is a^2 - b^2.

Also 64 - 49 (as 64 are both perfect squares).

The way to factor is by using the identity:

a^2 - b^2 = (a - b)(a + b) ( a + in one parentheses and - in the other)

Examples:

x^2 - 4y^2 = (x - 2y)(x + 2y) [ x is the square root of x^2 and 2y is square root of 4y^2)

144 - 16 = (12 - 4)(12 + 4)

9x^2 - 36y^2 = (3x - 6y)(3x + 6y)

Answer 2

A difference of squares has the following form . Any two perfect squares connected by subtraction can be factored.

It factors to (a+b)(a-b).

Explanation:

A binomial is an expression with only terms where at least one is a term with a variable. When we can factor for difference of squares, we can have two variable terms or just one with a constant.

A difference of squares has the following form . Any two perfect squares connected by subtraction can be factored.

It factors to (a+b)(a-b).