Difference of Two Squares

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What is the Difference of Two Squares?

Back

The Difference of Two Squares is a mathematical identity that states: a² - b² = (a + b)(a - b). It is used to factor expressions that are the difference between two perfect squares.

Tags

CCSS.HSA.APR.C.4

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.

Tags

CCSS.6.EE.A.1

Front

Factor the expression: x² - 9

Back

(x + 3)(x - 3)

Tags

CCSS.HSA.APR.C.4

Front

Factor the expression: 25x² - 36y²

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(5x + 6y)(5x - 6y)

Tags

CCSS.HSA.APR.C.4

Front

Factor the expression: 64x² - 81y²

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(8x + 9y)(8x - 9y)

Tags

CCSS.HSA.APR.C.4

Front

Factor the expression: 4x² - 16

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4(x + 2)(x - 2)

Tags

CCSS.HSA.APR.C.4

Front

Factor the expression: x² - 144

Back

(x + 12)(x - 12)

Tags

CCSS.HSA.APR.C.4

Front

What is the formula for factoring the Difference of Two Squares?

Back

The formula is a² - b² = (a + b)(a - b).

Tags

CCSS.HSA.APR.C.4

Front

Give an example of a Difference of Two Squares problem.

Back

Example: Factor x² - 25. Solution: (x + 5)(x - 5).

Tags

CCSS.HSA.APR.C.4

Front

What are the steps to factor a Difference of Two Squares?

Back

1. Identify the two squares. 2. Apply the formula a² - b² = (a + b)(a - b).

Tags

CCSS.HSA.APR.C.4