Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper.
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Transcript of Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper.
Factor.
64x81 2
8-5 Factoring Differences of Squares
Algebra 1 Glencoe McGraw-Hill Linda Stamper
a
The area of the large square is a2.
a
b
b
The area of the small square is b2.
If the small square is cut from the large square
Difference of Two Squares
the remaining region has an area of a2 − b2.
a
a
b
b
Difference of Two Squares
What are the dimensions of the irregular region? a - b
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
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?
22 ba
Difference of Two Squares
22 bababa
factors
product
9x2
Recognizing a difference of two squares may help you to factor - notice the sum and difference pattern. 22 3x 3x3x
64x81 2 222 8x9 8x98x9
No middle term – check if first and last terms are squares. Sign is negative.
Check using FOIL!
Factor.
5x5x 25x2 6x6x 36x2
2x22x2 4x4 2 4x34x3 16x9 2
4x24x2 16x4 2
5x45x4 25x16 2 Sign must be negative!
16x49 2 prime
Example 1 100y9 2
10y310y3
Check using FOIL!
Factor.
Example 2 81m64 2
9m89m8
Example 3
36m49 2 6m76m7
Example 4 9n1212
3n113n11
Example 5 144y16 2
12y412y4
Example 6 25x36 2
5x65x6
Remember to factor completely.
Write problem. 100x25 2
No middle term – check if first and last terms are squares.
2x2x25
Factor – must use parentheses.
Check using FOIL!
Factor out the GMF. 4x25 2
100x25 2 222 10x5
10x510x5 2x5 2x5 2x2x25
Sometimes you may need to apply several different factoring techniques.
15x5x15x5 23
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.
3xx3x5 23
3x3xx5 23
1x31xx5 22
3x1x5 2
Factor the difference of squares.
3x1x1x5
Example 7 1y4
1y1y 22
1y1y1y2
Factor.Example 8
44 b4a4
44 ba4
Example 9
81x4
9x9x 22
Example 10
2222 baba4
bababa4 22
9x9x9x2
120x24x30x6 23 20x4x5x6 23
20x5x4x6 23
4x54xx6 22
5x4x6 2
5x2x2x6
Use factoring to solve the equation. Remember to set each factor equal to zero and then solve!
081y16 2
Example 11 Example 12
169
x2
0x4x9 3
Example 13 Example 14 120d24d30d6 23
Use factoring to solve the equation. Remember to set each factor equal to zero and then solve!
081y16 2
09y4 or 09y4
49
y
9y4
49
y
Example 11 Example 12
09y49y4
9y4
169
x2
043
x or 043
x
43
y 43
y
043
x43
x
0169
x2
Use factoring to solve the equation. Remember to set each factor equal to zero and then solve!
0x4x9 3
02x3 or 02x3or0x
32
x
2x3
32
x
Example 13
02x32x3x
2x3
04x9x 2
0x
Use factoring to solve the equation. Remember to set each factor equal to zero and then solve!
Example 14
120d24d30d6 23
020d4d5d6 23
020d5d4d6 23
04d54dd6 22
05d4d6 2
05d2d2d6
05d or 02dor02dor06 2d 5d 2d 06
0120d24d30d6 23
8-A11 Pages 451-452 # 11–30,40,49-52.