Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper.

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Presentation transcript:

Factor.

8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper

a The area of the large square is a 2. a b b The area of the small square is b 2. If the small square is cut from the large square Difference of Two Squares the remaining region has an area of a 2 − b 2.

a a b b Difference of Two Squares What are the dimensions of the irregular region? a - b Cut the irregular region into two congruent pieces. Rearrange the two pieces to form a rectangle.

a a b b Difference of Two Squares What are the dimensions of the irregular region? a - b Cut the irregular region into two congruent pieces. Rearrange the two pieces to form a rectangle.

Difference of Two Squares What are the dimensions of the irregular region? Cut the irregular region into two congruent pieces. Rearrange the two pieces to form a rectangle.

Difference of Two Squares What are the dimensions of the irregular region? Cut the irregular region into two congruent pieces. Rearrange the two pieces to form a rectangle.

Difference of Two Squares What are the dimensions of the irregular region? Cut the irregular region into two congruent pieces. Rearrange the two pieces to form a rectangle.

Difference of Two Squares What are the dimensions of the irregular region? Cut the irregular region into two congruent pieces. Rearrange the two pieces to form a rectangle. a a - b b a + b (a + b) (a – b) What is the area?

Difference of Two Squares factors product Recognizing a difference of two squares may help you to factor - notice the sum and difference pattern. No middle term – check if first and last terms are squares. Sign is negative. Check using FOIL!

Factor. Sign must be negative! prime

Example 1 Check using FOIL! Factor. Example 2 Example 3 Example 4 Example 5 Example 6

Remember to factor completely. Write problem. No middle term – check if first and last terms are squares. Factor – must use parentheses. Check using FOIL! Factor out the GMF.

Sometimes you may need to apply several different factoring techniques. Group terms with common factors. Factor each grouping. Factor the common binomial factor. Check – Multiply the factors together using FOIL. The problem. Factor out the GMF. Factor the difference of squares.

Example 7 Factor. Example 8 Example 9 Example 10

Use factoring to solve the equation. Remember to set each factor equal to zero and then solve! Example 11 Example 12 Example 13 Example 14

Use factoring to solve the equation. Remember to set each factor equal to zero and then solve! Example 11 Example 12

Use factoring to solve the equation. Remember to set each factor equal to zero and then solve! Example 13

Use factoring to solve the equation. Remember to set each factor equal to zero and then solve! Example 14

8-A11 Pages # 11–30,40,49-52.