Question

Circle the special binomials below that represent a difference of squares and can be factored into two new binomials. Then write the two new binomials. If there is not a difference of squares, then don’t circle the problem, and write “already factored” on the line below itA) x^2-49B) x^2+25C) 4x^2-64D) 9x^2+49E) 10x^2-49

Answer 1

The difference of two squares means each term has a square root and the sign between them must be (-)

`a^2-b^2=(a+b)(a-b)`

Let us check each answer

A)

`x^2-49`

The first term has a square root, the second term has a square root, and the sign between them is (-)

Then it is a difference of 2 squares

`x^2-49=(x+7)(x-7)`

Circle answer A

B)

`x^2+25`

Since the sign between the 2 terms is (+), then

It is not a difference of 2 squares

C)

`4x^2-64`

Since the first term has a square root, the second term has a square root, and the sign between them is (-)

`4x^2-64=(2x+8)(2x-8)`

Then it is a difference of two squares

Circle answer C

D)

`9x^2+49`

Since the sign between the 2 terms is (+), then

It is not a difference between 2 squares

E)

`10x^2-49`

Since there is no square root for 10, then the first term is not a square number

It is not a difference of two squares

The correct answer is A and C