Difference of Squares

Front

What is the Difference of Squares?

Back

The Difference of Squares is a mathematical identity that states: a² - b² = (a + b)(a - b). It applies when you have a square term subtracted from another square term.

Front

Can 9n² + 1 be factored using the Difference of Squares?

Back

No, 9n² + 1 cannot be factored using the Difference of Squares because it is a sum of squares.

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Can x² + 81 be factored using the Difference of Squares?

Back

No, x² + 81 cannot be factored using the Difference of Squares because it is a sum of squares.

Front

What is the factored form of r² - 9t²?

Back

The factored form of r² - 9t² is (r + 3t)(r - 3t).

Front

What is the factored form of q² - 121?

Back

The factored form of q² - 121 is (q + 11)(q - 11).

Front

Can 4m² + 49 be factored using the Difference of Squares?

Back

No, 4m² + 49 cannot be factored using the Difference of Squares because it is a sum of squares.

Front

What is an example of a Difference of Squares?

Back

An example of a Difference of Squares is 16 - x², which factors to (4 + x)(4 - x).

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What types of expressions can be factored using the Difference of Squares?

Back

Expressions that can be factored using the Difference of Squares must be in the form a² - b², where both a and b are real numbers.

Front

Is the expression 25 - y² a Difference of Squares?

Back

Yes, 25 - y² is a Difference of Squares and factors to (5 + y)(5 - y).

Front

What is the first step in factoring a Difference of Squares?

Back

The first step is to identify if the expression is in the form a² - b².