10.6 – Special Products of Polynomials Multiplying Two Binomials using FOIL 7 4 x x 3 4 x x F irst terms L ast terms I nner terms O uter terms 2 x 4 x 7 x 28 2 x 7 x 12 2 x 3 x 28 2 x 4 x 3 x 12
10.6 – Special Products of Polynomials Multiplying Two Binomials using FOIL First termsLast termsInner termsOuter terms.
Jan 18, 2016
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10.6 – Special Products of Polynomials
Multiplying Two Binomials using FOIL
7 4x x
3 4x x
First terms Last termsInner termsOuter terms
2x 4x 7x 28
2x 7x 12
2x 3x 28
2x 4x 3x 12
Multiplying Two Binomials using FOIL
6 2 3 3x x
2 1 5 6x x
First terms Last termsInner termsOuter terms
210x 12x 5x 6
210x 7x 6
218x 18x 6x 6
218x 24x 6
10.6 – Special Products of Polynomials
Multiplying Two Binomials using FOIL
22 3 4y y
First terms Last termsInner termsOuter terms
22 4y
32y 28y 3y 12
32y 28y 3y 12
2 24 4y y
4y 24y 16 24y 4y 28y 16
10.6 – Special Products of Polynomials
Squaring Binomials
25r 5 5r r 2r
2 10 25r r
22 9x 2 9 2 9x x
24x24 36 81x x
23 4t 29t
29 24 16t t
5r 5r 25
18x 18x 81
2 12t 16
10.6 – Special Products of Polynomials
Squaring Binomials
22 3x 24x
2 14 49x x 27x 2x
24 12 9x x
25 8x 225x
225 80 64x x
22x y 2x 2 24 4x xy y
2 7x 49
2 6x 9
2 40x 64
2 2xy 24y
10.6 – Special Products of Polynomials
Squaring Binomials
24 5x 216x
216 40 25x x
2 2 2
2 2 2
2
2
a b a ab b
a b a ab b
23 6x 29x
29 36 36x x
2 20x 25
2 18x 36
10.6 – Special Products of Polynomials
Multiplying the Sum and Difference of Two Binomials
2 2a b a b a b
9 9x x 2x
9 9x x 2 81x
2 81x
3 5 3 5x x
3 5 3 5x x 29x 29 25x
29 25x
9x 9x 81
15x 15x 25
10.6 – Special Products of Polynomials
10.7 – Dividing Polynomials
Dividing by a Monomial
where 0a b a b
cc c c
3 2
2
25 5
5
x x
x
3
2
25
5
x
x
5x
2
2
5
5
x
x
1
Dividing by a Monomial
where 0a b a b
cc c c
8 6 4
3
21 9 12
3
x x x
x
8
3
21
3
x
x
57x
6
3
9
3
x
x
4
3
12
3
x
x
33x 4x
10.7 – Dividing Polynomials
Dividing by a Monomial
7 2 224 12 4 4x x x x 7 2
2
24 12 4
4
x x x
x
7
2
24
4
x
x
56x
2
2
12
4
x
x
2
4
4
x
x
3 1
x
10.7 – Dividing Polynomials
Dividing by a Monomial
3 312 18 6
3
x y xy y
xy
3 312
3
x y
xy
2 24x y
18
3
xy
xy
6
3
y
xy
62
x
10.7 – Dividing Polynomials
285
5
Review of Long Division
783 4
4 7835 2855
2535
7
350
438362
19
3
5
203
10.7 – Dividing Polynomials
Dividing by a Polynomial Other than a Monomial
2 12 35 5x x x 25 12 35x x x
(Long Division)
10.7 – Dividing Polynomials
35125 2 xxx
x
xx 52 x7 35
7
357 x
0
5x 7x 35122 xx
10.7 – Dividing Polynomials
Dividing by a Polynomial Other than a Monomial
28 2 7 2 1x x by x
22 1 8 2 7x x x
(Long Division)
10.7 – Dividing Polynomials
72812 2 xxx
x4
xx 48 2 x6 7
3
36 x
4
12 x
12
434
xx 728 2 xx
12
4
x
10.7 – Dividing Polynomials
Dividing by a Polynomial Other than a Monomial
215 2
3
x
x
23 2 0 15x x x
(Long Division)
10.7 – Dividing Polynomials
15023 2 xxx
x2
xx 62 2 x6 15
6
186 x
3
3x
3
362x
x 152 2 x
3
3
x
10.7 – Dividing Polynomials
End of Slide ShowEnd of Slide Show
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