Difference of Two Squares

Front

What is the difference of two squares formula?

Back

The difference of two squares formula states that a^2 - b^2 = (a + b)(a - b).

Front

Can you provide an example of the difference of two squares?

Back

An example is 64x^2 - 81y^2, which factors to (8x + 9y)(8x - 9y).

Front

What types of expressions can be factored using the difference of two squares?

Back

Expressions that can be factored using the difference of two squares must be in the form a^2 - b^2, where both a and b are perfect squares.

Front

Is 16x^3 - 25y^2 factorable using the difference of two squares? Why or why not?

Back

No, because 16x^3 is not a perfect square; it must be in the form of a^2.

Front

What is the result of factoring 4x^2 - 25?

Back

The result is (2x + 5)(2x - 5).

Front

What is the sum of squares, and can it be factored?

Back

The sum of squares, such as 49x^2 + 16, cannot be factored over the real numbers.

Front

What is a perfect square?

Back

A perfect square is an expression that can be written as the square of a binomial, such as (a + b)^2 = a^2 + 2ab + b^2.

Front

How do you identify a difference of squares in an expression?

Back

Look for two terms that are both perfect squares separated by a subtraction sign.

Front

What is the first step in factoring a difference of two squares?

Back

Identify the two perfect squares and apply the formula a^2 - b^2 = (a + b)(a - b).

Front

Can the expression 36 - x^2 be factored? If so, how?

Back

Yes, it can be factored as (6 + x)(6 - x).