Objectives

Factor perfect-square trinomials.Factor the difference of two

squares.

Page 452 – Factoring Special Polynomials

Glossary Terms

perfect-square trinomial – a trinomial in the form a² + 2ab + b²

difference of two squares – a polynomial in the form a² - b²

Rules and Properties

Rule for Factoring a Perfect-Square Trinomial

a2 + 2ab + b2 = (a + b)(a + b) = (a + b) 2

a2 – 2ab + b2 = (a – b)(a – b) = (a – b) 2

How to tell if it is a perfect square trinomial

4x² + 12x + 91) Are there three terms (trinomial)? yes

2) Is the first term a perfect square? yes

3) Is the last term a perfect square? yes

4) Is the square root of the first term, times the square root of the last term, times 2, equalto the middle term? yes

Since the answer to all the questions is yes, 4x² + 12x + 9 is a perfect square trinomial.

To factor a perfect square trinomial4x² + 12x + 9

1) Write the square root of the first term.

2x

2) Write the sign of the middle term.

+

3) Write the square root of the last term.

3

4) Put parentheses around it and square it.

( )²

State whether each term is a perfect square trinomial. If not,

explain.

x² + 8x + 16

yes

3x² + 16x + 16

no , the first term is not a perfect square

x² + 3x + 9

no , the square root of the first times the square root of the last times 2 does not equal the middle term

x² + 10x - 25

no , the last term must always be positive

Factor each expression

x² - 10x + 25

x - 5( )²

49y4 + 14y² + 1

7y + 1( )²

Rules and PropertiesRule for Factoring a Difference of Two Squares

a2 – b2 = (a + b)(a – b)

How to tell if it’s the difference of 2 squares

4y² - 49

1) Are there two terms? yes

2) Is the first term a perfect square? yes

3) Is the last term a perfect square? yes

4) Is there a minus sign between them? yes

Since the answer to all the questions is yes, 4y² - 49 is the difference of two squares.

How to factor the difference of two squares.

4x² - 49

1) Write the square root of the first term.

2x

2) Plus

+

3) Write the square root of the last term.

9

4) Times (Use parentheses)

( ) (

5) Write the square root of the term.

2x

6) Minus

-

7) Write the square root of the last term and close the parentheses.

9)

Tell whether each of the following is the difference of two squares

4a² - 25yes

9x² - 15

no, the last term, 15, is not a perfect square

16r² + 49

no, there is not a minus sign between them

Factor each expression

x² - 4

(x + 2) ( x - 2)

36a² - 49b²

(6a + 7b) (6a - 7b)

25w² - 81

(5w + 9) (5w – 9)

ASSIGNMENT

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