How do you determine if a factoring problem will use the difference of two​ squares? Choose the correct answer below.

Question

How do you determine if a factoring problem will use the difference of two squares?
Choose the correct answer below.

A.
The problem will have two terms. It will be in the form a^3-b^3
The coefficients and variables for the first and second terms are both perfect squares.

B.
The problem will have two terms. It will be in the form a^2-b^2
The coefficients and variables for the first and second terms are both perfect squares.

C. The problem will have two terms. It will be in the form a^3+b^3
The coefficients and variables for the first and second terms are both perfect squares.

D. The problem will have three terms. It will be in the form a^2+2ab+b^2
2. The coefficients and variables for the first and last terms are both perfect squares.

Answer 1

Difference in perfect squares are usually in the form          a² - b²

 

where   a is a square-root of a² , and b is a square-root of b². 

 

 

Here is the factoring.

 

a² - b² = (a - b)(a + b)

 

          = (√a² - √b²)(√a² + √b²)

 

 

When you expand back using FOIL method, you get

 

          = √(a⁴) - √(b⁴)

      

          = a² - b²