Question

3
select the correct answer.
consider polynomials p and q.
p = 8y⁴ + 6y³ + 8y
q = (5y² − 4y)(3y² + 7)
which operation results in an expression equivalent to 23y⁴ − 6y³ + 35y² − 20y?
a. pq
b. p − q
c. p + q
d. q − p

Explanation:

Step1: Expand Q

First, expand \( Q=(5y^2 - 4y)(3y^2 + 7) \) using the distributive property (FOIL method for binomials, extended for polynomials).

$$
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$$

Step2: Check each operation

• Option A: \( PQ \)

Multiplying \( P = 8y^4 + 6y^3 + 8y \) and \( Q = 15y^4 - 12y^3 + 35y^2 - 28y \) will result in a polynomial of degree \( 8 \) (since \( y^4 \times y^4 = y^8 \)), but the target expression is degree \( 4 \). So A is incorrect.

• Option B: \( P - Q \)

Subtract \( Q \) from \( P \):

$$
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$$

This does not match the target. So B is incorrect.

• Option C: \( P + Q \)

Add \( P \) and \( Q \):

$$
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$$

This matches the target expression.

• Option D: \( Q - P \)

Subtract \( P \) from \( Q \):

$$
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$$

This does not match the target. So D is incorrect.

Answer:

C. \( P + Q \)