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Simplify Expressions with Multiplication
A. Simplify (–2a3b)(–5ab4).
(–2a3b)(–5ab4) = (–2 ● a ● a ● a ● b) ●
(–5 ● a ● b ● b ● b ● b)
Definition of exponents
= –2(–5) ● a ● a ● a ● a
●b●b●b●b●b
Commutative Property
= 10a4b5
Answer: 10a4b5
Definition of exponents
Simplify Expressions with Multiplication
B. Simplify (3a5)(c–2)(–2a–4b3).
(3a5)(c–2)(–2a–4b3)
Definition of negative
exponents
Definition of exponents
Simplify Expressions with Multiplication
Cancel out common factors.
Definition of exponents and
fractions
Answer:
A. Simplify (–3x2y)(5x3y5).
A. –15x5y6
B. –15x6y5
C. 15x5y6
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
B. Simplify (4x–2)(xy–3).
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
0%
0%
A
B
0%
C
0%
D
Simplify Expressions with Division
Subtract exponents.
Remember that a simplified
expression cannot contain
negative exponents.
Answer:
A. x10
B. x21
0%
C. x4
D.
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Simplify Expressions with Powers
A. Simplify (–3c2d5)3.
(–3c2d5)3 = (–3)3(c2)3(d5)3
= –27c6d15
Answer: –27c6d15
Power of a power
Simplify.
Simplify Expressions with Powers
B.
Power of a quotient
Power of a product
(–2)5 = –32
Answer:
A. Simplify (x3)5.
A. x15
B. x8
C. x2
D.
0%
1.
2.
3.
4.
A
A
B
C
D
B
C
D
B. Simplify
.
A.
0%
B.
C.
D.
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Simplify Expressions Using Several
Properties
Method 1 Raise the numerator and the denominator to
the fifth power before simplifying.
Simplify Expressions Using Several
Properties
Answer:
Simplify Expressions Using Several
Properties
Method 2
Simplify the fraction before raising to the
fifth power.
Simplify Expressions Using Several
Properties
Answer:
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
0%
0%
A
B
0%
C
0%
D
BIOLOGY There are about 5 × 106 red blood cells in
one milliliter of blood. A certain blood sample
contains 8.32 × 106 red blood cells. About how
many milliliters of blood are in the sample?
Divide the number of red blood cells in the sample by
the number of red blood cells in 1 milliliter of blood.
← number of red blood cells in sample
← number of red blood cells in 1 milliliter
Answer: There are about 1.66 milliliters of blood in the
sample.
BIOLOGY A petri dish started
with 3.6 × 105 germs in it. A half
hour later, there are 7.2 × 107.
How many times as great is the
amount a half hour later?
A. 2
B. 20
0%
0%
D
0%
C
0%
B
D. 2.592 × 1013
A
B
C
D
A
C. 2 × 102
A.
B.
C.
D.
Simplify Polynomials
A. Simplify (2a3 + 5a – 7) – (a3 – 3a + 2).
(2a3 + 5a – 7) – (a3 – 3a + 2)
Distribute the –1.
Group like terms.
= a3 + 8a – 9
Answer: a3 + 8a – 9
Combine like terms.
Simplify Polynomials
B. Simplify (4x2 – 9x + 3) + (–2x2 – 5x – 6).
(4x2 – 9x + 3) + (–2x2 – 5x – 6)
Remove parentheses.
Group like terms.
= 2x2 – 14x – 3
Answer: 2x2 – 14x – 3
Combine like terms.
A. Simplify (3x2 + 2x – 3) – (4x2 + x – 5).
A. 7x2 + 3x – 8
B. –x2 + 3x – 8
0%
C. –x2 + 3x + 2
D. –x2 + x + 2
1.
2.
3.
4.
A
B
C
D
A
B
C
D
B. Simplify (–3x2 – 4x + 1) – (4x2 + x – 5).
A. 9x2 + 6x + 7
B. –7x2 – 5x + 6
0%
C. 3x2 – 6x + 7
D. 3x2 – 2x + 6
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Simplify Using the Distributive Property
Find –y(4y2 + 2y – 3).
–y(4y2 + 2y – 3) = –y(4y2) –y(2y) – y(–3)
Distributive Property
= –4y3 – 2y2 + 3y
Multiply the monomials.
Answer: –4y3 – 2y2 + 3y
Find –x(2x3 – 2x + 5).
A. –3x2 – 2x + 5
B. –4x4 – 3x2 – 6x
C. –3x4 + 2x2 – 5x
D. –3x4 – 2x3 + 5x
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Multiply Polynomials
Find (a2 + 3a – 4)(a + 2).
(a2 + 3a – 4)(a + 2)
Distributive Property
Distributive Property
Multiply monomials.
= a3 + 5a2 + 2a – 8
Answer: a3 + 5a2 + 2a – 8
Combine like terms.
Find (x2 + 3x – 2)(x + 4).
A. x3 + 7x2 + 10x – 8
B. x2 + 4x + 2
D. x3 + 7x2 + 14x – 8
A.
B.
C.
D.
A
B
C
D
0%
D
0%
C
A
C. x3 + 3x2 – 2x + 8
0%
B
0%
Animation: Multiply Polynomials