factor.. 8-5 factoring differences of squares algebra 1 glencoe mcgraw-hilllinda stamper
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![Page 1: Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bfe41a28abf838cb58a4/html5/thumbnails/1.jpg)
Factor.
64x81 2
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8-5 Factoring Differences of Squares
Algebra 1 Glencoe McGraw-Hill Linda Stamper
![Page 3: Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bfe41a28abf838cb58a4/html5/thumbnails/3.jpg)
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.
![Page 4: Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bfe41a28abf838cb58a4/html5/thumbnails/4.jpg)
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.
![Page 5: Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bfe41a28abf838cb58a4/html5/thumbnails/5.jpg)
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.
![Page 6: Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bfe41a28abf838cb58a4/html5/thumbnails/6.jpg)
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.
![Page 7: Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bfe41a28abf838cb58a4/html5/thumbnails/7.jpg)
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.
![Page 8: Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bfe41a28abf838cb58a4/html5/thumbnails/8.jpg)
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.
![Page 9: Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bfe41a28abf838cb58a4/html5/thumbnails/9.jpg)
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
![Page 10: Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bfe41a28abf838cb58a4/html5/thumbnails/10.jpg)
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!
![Page 11: Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bfe41a28abf838cb58a4/html5/thumbnails/11.jpg)
Factor.
5x5x 25x2 6x6x 36x2
2x22x2 4x4 2 4x34x3 16x9 2
4x24x2 16x4 2
5x45x4 25x16 2 Sign must be negative!
16x49 2 prime
![Page 12: Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bfe41a28abf838cb58a4/html5/thumbnails/12.jpg)
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
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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
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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
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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
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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
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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
![Page 18: Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bfe41a28abf838cb58a4/html5/thumbnails/18.jpg)
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
![Page 19: Factor.. 8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bfe41a28abf838cb58a4/html5/thumbnails/19.jpg)
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
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8-A11 Pages 451-452 # 11–30,40,49-52.