1. Page 452 – Factoring Special
Polynomials
Objectives
Factor perfect-square trinomials.
Factor the difference of two squares.

2. Glossary Terms
perfect-square trinomial – a trinomial in the form a² + 2ab + b²
difference of two squares – a polynomial in the form a² - b²

3. 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

4. How to tell if it is a perfect square trinomial
4x² + 12x + 9
1) 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, equal
to the middle term?
yes
Since the answer to all the questions is yes,
4x² + 12x + 9 is a perfect square trinomial.

5. To factor a perfect square trinomial
4x² + 12x + 9
1) Write the square root of the first term.
2) Write the sign of the middle term.
3) Write the square root of the last term.
4) Put parentheses around it and square it.
( )² 2x + 3

6. State whether each term is a perfect square trinomial. If not, explain.
x² + 8x + 16
3x² + 16x + 16
yes no
, the first term
is not a perfect
square
x² + 3x + 9
x² + 10x - 25
, the square root
of the first times
the square root of
the last times 2
does not equal the
middle term no
, the last term
must always be
positive no

7. Factor each expression
x² - 10x + 25
( )² x - 5
49y4 + 14y² + 1
( )² 7y + 1

8. Rules and Properties Rule for Factoring a Difference of Two Squares
a2 – b2 = (a + b)(a – b)

9. 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.

10. How to factor the difference of two squares.
4x² - 49
1) Write the square root of the first term.
2) Plus
3) Write the square root of the last term.
4) Times (Use parentheses)
5) Write the square root of the term.
6) Minus
7) Write the square root of the last term and close
the parentheses.
( ) ( 2x + 9 2x - 9)

11. Tell whether each of the following is the difference of two squares
yes
9x² - 15
the last term, 15, is not a perfect
square
no,
16r² + 49
there is not a
minus sign
between them
no,

12. Factor each expression+ 2
) ( x - 2)
36a² - 49b²
(6a + 7b
) ( 6a -
7b)
25w² - 81
(5w + 9) (5w – 9)

13. ASSIGNMENT
Page 455 – 457
# 18 – 38, 44 – 48,