warm-up: simplify. 1.6 (3x - 5) = 18x - 30 2.4 (2x + 10) = 8x + 40 3.9y - 3y = 6y 4.7a + 4b + 3a -...
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Warm-up: Simplify.1. 6 (3x - 5) =
18x - 30
2. 4 (2x + 10) =
8x + 40
3. 9y - 3y =
6y
4. 7a + 4b + 3a - 2b =
10a + 2b
5. 4 (3x + 2) + 2 (x + 3) =
14x + 14
Multiplying PolynomialsObjective:
•Multiply two monomials
•Multiply a monomial by a polynomial
Why are the following not monomials?
x + yaddition
division
2 - 3a
subtraction
x
y
Multiplying MonomialsWhen multiplying monomials, you
ADD the exponents.
1) x2 • x4
x2+4
x6
2) 2a2y3 • 3a3y4
6a5y7
Simplify m3(m4)(m)
1. m7
2. m8
3. m12
4. m13
Power of a PowerWhen you have an exponent with an
exponent, you multiply those exponents.
1) (x2)3
x2• 3
x6
2) (y3)4
y12
Simplify (p2)4
1. p2
2. p4
3. p8
4. p16
Power of a ProductWhen you have a power outside of the
parentheses, everything in the parentheses is raised to that power.
1) (2a)3
23a3
8a3
2) (3x)2
9x2
Simplify (4r)3
1. 12r3
2. 12r4
3. 64r3
4. 64r4
Power of a MonomialThis is a combination of all of the other
rules.
1) (x3y2)4
x3• 4 y2• 4
x12 y8
2) (4x4y3)3
64x12y9
Simplify (3a2b3)4
1. 12a8b12
2. 81a6b7
3. 81a16b81
4. 81a8b12
add the exponents!
1) Simplify: 5(7n - 2)
Use the distributive property.
5 • 7n
35n - 10
Review: When multiplying variables,
- 5 • 2
3(8 12)
4a a 2) Simplify:
6a2 + 9a
3) Simplify: 6rs(r2s - 3) 6rs • r2s
6r3s2 - 18rs
38
4a a
312
4a
- 6rs • 3
4) Simplify: 4t2(3t2 + 2t - 5)
12t4
5) Simplify: - 4m3(-3m - 6n + 4p)
12m4
+ 8t3 - 20t2
+ 24m3n - 16m3p
6) Simplify: (27x2 - 6x + 12)
16x3 - 28x2 + 4x
Fooled ya, didn’t I?!? Ha! Ha!
Here’s the real answer!
-9x3 + 2x2 - 4x
x3
Simplify 4y(3y2 – 1)
1. 7y2 – 1
2. 12y2 – 1
3. 12y3 – 1
4. 12y3 – 4y
Simplify -3x2y3(y2 – x2 + 2xy)
1. -3x2y5 + 3x4y3 – 6x3y4
2. -3x2y6 + 3x4y3 – 6x2y3
3. -3x2y5 + 3x4y3 – 6x2y3
4. 3x2y5 – 3x4y3 + 6x3y4
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