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Multiplying Polynomials and Simplifying Expressions Answers

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The variables A, B, and C represent polynomials where A = x2, B = 3x + 2, and C = x – 3. What is AB – C2 in simplest form?

A
3x3 + 2x2 – x + 3
B
3x3 + 2x2 – x – 3
C
3x3 + x2 – 6x + 9
D
3x3 + x2 + 6x – 9
2
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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
3

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
4

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
5

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.
6

The polynomial x3 + 8 is equal to

A
(x + 2)(x2 – 2x + 4).
B
(x – 2)(x2 + 2x + 4).
C
(x + 2)(x2 – 2x + 8).
D
(x – 2)(x2 + 2x + 8).
7

What is the product?(4y − 3)(2y2 + 3y − 5)

A
8y3 + 3y + 15
B
8y3 − 23y + 15
C
8y3 − 6y2 − 17y + 15
D
8y3 + 6y2 − 29y + 15
8

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
9

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
10

What is the product?(x − 3)(2x2 − 5x + 1)

A
2x3 − x2 + 16x + 3
B
2x3 − 11x2 + 16x + 3
C
2x3 − 11x2 + 16x − 3
D
2x3 − x2 + 16x − 3

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