AnswersAlgebra I CR GTMultiplying Polynomials and Simplifying Expressions

Multiplying Polynomials and Simplifying Expressions Answers

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Sharina simplified the expression 3(2x – 6 – x + 1)2 – 2 + 4x. In Step 1 she simplified within the parentheses. In Step 2 she expanded the exponent.

Question illustration
A
Simplify the expression by adding and subtracting from left to right.
B
Combine like terms within the parentheses.
C
Combine all x-terms.
D
Distribute the 3 to each term in the parentheses by multiplying.
2
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Iliana multiplied 3p – 7 and 2p2 – 3p – 4. Her work is shown in the table.

Question illustration
A
6p3 + 23p2 + 9p + 28
B
6p3 – 23p2 – 9p + 28
C
6p3 – 23p2 + 9p + 28
D
6p3 + 23p2 – 9p + 28
3

Chin made an error in his chart showing the multiplication of the binomial by the trinomial.

Question illustration
A
The expression 3x3 should be 3x2.
B
The expression 6x should be 6xy.
C
The expression x2y should be x2y2.
D
The expression 4y should be 4y2.
4

Simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2. Which statements are true about the process and simplified product? Select three options.

A
The term –2(x – 2)2 is simplified by first squaring the expression x – 2.
B
The simplified product is a binomial.
C
After multiplying, the like terms are combined by adding and subtracting.
D
The parentheses are eliminated through multiplication.
E
The final simplified product is –28x2 +8x – 8.
5

The product of a binomial and a trinomial is x 3 + 3 x 2 − x + 2 x 2 + 6 x − 2. Which expression is equivalent to this product after it has been fully simplified?

A
x3 + 5x2 + 5x – 2
B
x3 + 2x2 + 8x – 2
C
x3 + 11x2 – 2
D
x3 + 10x2 – 2
6

Use the chart to multiply the binomial by the trinomial.

Question illustration
A
15y3 + 17y2 + 22y + 15
B
6y3 + 17y2 + 22y + 15
C
6y3 + 20y2 + 22y + 15
D
6y3 + 17y2 + 22y + 25
7

What is the product of (3a + 2)(4a2 – 2a + 9)?

A
12a3 − 2a + 18
B
12a3 + 6a + 9
C
12a3 − 6a2 + 23a + 18
D
12a3 + 2a2 + 23a + 18
8

Use the chart to multiply the binomial by the trinomial.

Question illustration
A
y3 + 27
B
y3 – 27
C
y3 – 6y2 + 27
D
y3 + 6y2 + 27
9

Using the distributive property, Marta multiplied the binomial (2x + 3) by the trinomial (x2 + x – 2) and got the expression below.(2x)(x2) + (2x)(x) + (2x)(–2) + (3)(x2) + (3)(x) + (3)(–2)Which is the simplified product?

A
2x3 + 6x2 – x – 6
B
2x3 + x2 – x – 6
C
2x3 + 5x2 – x – 6
D
2x3 – x2 – 7x – 6
10

Using the distributive property to find the product (y−4x)(y2+4y+16) results in a polynomial of the form y3+4y2+ay−4xy2−axy−64x. What is the value of a in the polynomial?

A
4
B
8
C
16
D
32

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