Transcript Lesson 5.9

5.9 Multiplication of Monomials
and Binomials
Multiplying Monomial and
Polynomial
 We will use the distributive
property
 Multiply the numbers in front
 ADD any exponents (little
numbers) that have the same
letter
Example 1
2 x(5 x  3)
2 x  5x  2 x  3
10 x  6 x
2
Example 2
5 x (3 x  2)
2
5 x  3x  5 x  2
2
2
15 x  10 x
3
2
You Try
2b (3b  6)
2
2
2b  3b  2b  6
2
2
 6b  12b
4
2
2
Example 3
3a (5a  2a  7)
2
3
3a  5a  3a  2a  3a  7
2
3
2
2
 15a  6a  21a
5
3
2
Example 4
6a (2a  7 a  4)
3
3
6a  2a  6a  7 a  6a  4
3
3
3
3
12a  42a  24a
6
4
3
You Try
5a (8a  3a  4a )
2
4
2
5a  8a  5a  3a  5a  4a
2
4
2
2
 40a  15a  20a
6
4
2
3
Example 5
8 p (3q  2q p  2 p )
4
3
2
8 p  3q  8 p  2q p  8 p  2 p
4
3
2
24 pq  16q p  16 p
4
3
3
2
Example 6
 2 x (4 x  3x  7 xy  6)
3
2
 2 x  4 x  2 x  3x  2 x  7 xy  2 x  6
3
3
2
3
 8 x  6 x  14 x y  12 x
4
5
4
3
3
Example 7
5 y ( x  2 y  y  2 x  3 y )
2
3
5 y  x  5 y  2 y  5 y   y  5 y  2x  5 y  3y
2
 5 yx  10 y  5 y  10 yx  15 y
2
3
4
3
You Try!
4 z (8 z  4 x  9 xz  2 xz  5)
2
3
2
2
4 z  8 z  4 z  4 x  4 z  9 xz  4 z  2 xz  4 z  5
2
3
2
2
2
2
2
32 z  16 z x  36 z x  8 xz  20 z
5
2 2
4
3
2
2
Assignment

Pg. 242 2-20 even
5.9 Continued
Multiplying Binomials
 We
will use the FOIL method
F→ First terms
(a+b)(c+d)
O → Outer terms
(a+b)(c+d)
I → Inner terms
(a+b)(c+d)
L → Last terms
(a+b)(c+d)
Example 7
O – OUTSIDE
F – FIRST
(x + 6)(x – 6)
I – INSIDE
L – LAST
1: multiply F: 𝒙 ∙ 𝒙
2: multiply O: 𝒙 ∙ −𝟔
3: multiply I: 𝟔 ∙ 𝒙
4: multiply L: 𝟔 ∙ −𝟔
𝒙𝟐 − 𝟔𝒙 + 𝟔𝒙 − 𝟑𝟔
𝒙𝟐 − 𝟑𝟔
Example 8
(x + 3)(x – 2)
𝑥 ∙ 𝑥 + 𝑥 ∙ −2 + 3 ∙ 𝑥 + 3 ∙ −2
2
𝑥 − 2𝑥 + 3𝑥 − 6
2
𝑥 + 1𝑥 − 6
Example 9
3
(x
3
5)(x
+
– 4)
3
3
3
3
𝑥 ∙ 𝑥 + 𝑥 ∙ −4 + 5 ∙ 𝑥 + 5
6
3
3
𝑥 − 4𝑥 + 5𝑥 − 20
6
3
𝑥 + 1𝑥 − 20
Example 10
(3x + 2)(x + 5)
3𝑥 ∙ 𝑥 + 3𝑥 ∙ 5 + 2 ∙ 𝑥 + 2 ∙ 5
2
3𝑥 + 15𝑥 + 2𝑥 + 10
2
3𝑥 + 17𝑥 + 10
Example 11
2
4𝑚 + 5𝑚𝑛 2𝑚𝑛 − 4𝑛
4𝑚2 ∙ 2𝑚𝑛 + 4𝑚2 ∙ −4𝑛 + 5𝑚𝑛 ∙ 2𝑚𝑛 + 5𝑚𝑛 ∙ −4𝑛
3
2
2 2
8𝑚 𝑛 − 16𝑚 𝑛 + 10𝑚 𝑛 − 20𝑚𝑛
2
Example 12
(3x2 + 4)(5x3 + 1)
2
3𝑥
∙
3
5𝑥
+
5
15𝑥
5
15𝑥
2
3𝑥
∙1+4∙
+
2
3𝑥
+
3
20𝑥
+
3
5𝑥
+4∙1
3
20𝑥
+4
2
3𝑥
+4
+
Assignment

Pg.242 22-42 even