warm-up: simplify. 1.6 (3x - 5) = 18x - 30 2.4 (2x + 10) = 8x + 40 3.9y - 3y = 6y 4.7a + 4b + 3a -...
TRANSCRIPT
![Page 1: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/1.jpg)
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
![Page 2: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/2.jpg)
Multiplying PolynomialsObjective:
•Multiply two monomials
•Multiply a monomial by a polynomial
![Page 3: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/3.jpg)
Why are the following not monomials?
x + yaddition
division
2 - 3a
subtraction
x
y
![Page 4: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/4.jpg)
Multiplying MonomialsWhen multiplying monomials, you
ADD the exponents.
1) x2 • x4
x2+4
x6
2) 2a2y3 • 3a3y4
6a5y7
![Page 5: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/5.jpg)
Simplify m3(m4)(m)
1. m7
2. m8
3. m12
4. m13
![Page 6: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/6.jpg)
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
![Page 7: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/7.jpg)
Simplify (p2)4
1. p2
2. p4
3. p8
4. p16
![Page 8: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/8.jpg)
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
![Page 9: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/9.jpg)
Simplify (4r)3
1. 12r3
2. 12r4
3. 64r3
4. 64r4
![Page 10: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/10.jpg)
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
![Page 11: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/11.jpg)
Simplify (3a2b3)4
1. 12a8b12
2. 81a6b7
3. 81a16b81
4. 81a8b12
![Page 12: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/12.jpg)
add the exponents!
1) Simplify: 5(7n - 2)
Use the distributive property.
5 • 7n
35n - 10
Review: When multiplying variables,
- 5 • 2
![Page 13: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/13.jpg)
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
![Page 14: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/14.jpg)
4) Simplify: 4t2(3t2 + 2t - 5)
12t4
5) Simplify: - 4m3(-3m - 6n + 4p)
12m4
+ 8t3 - 20t2
+ 24m3n - 16m3p
![Page 15: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/15.jpg)
6) Simplify: (27x2 - 6x + 12)
16x3 - 28x2 + 4x
Fooled ya, didn’t I?!? Ha! Ha!
Here’s the real answer!
-9x3 + 2x2 - 4x
x3
![Page 16: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/16.jpg)
Simplify 4y(3y2 – 1)
1. 7y2 – 1
2. 12y2 – 1
3. 12y3 – 1
4. 12y3 – 4y
![Page 17: 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](https://reader036.vdocument.in/reader036/viewer/2022062407/56649d9c5503460f94a859e2/html5/thumbnails/17.jpg)
Simplify -3x2y3(y2 – x2 + 2xy)
1. -3x2y5 + 3x4y3 – 6x3y4
2. -3x2y6 + 3x4y3 – 6x2y3
3. -3x2y5 + 3x4y3 – 6x2y3
4. 3x2y5 – 3x4y3 + 6x3y4