Multiply the following polynomials.

4a(a2 + 7a + 4)
A. 4a + 28a2 + 16a
B. 4a3 + 28a2 + 16a
C. 4a3 + 44a
D. 44a4

2 answers

The answer is B. 4a3 + 28a2 + 16a.

To multiply the polynomials, you use the distributive property, which states that a(b+c) = ab + ac. In this case, we are multiplying the polynomial 4a by the polynomial (a2 + 7a + 4):

4a(a2 + 7a + 4) = 4a(a2) + 4a(7a) + 4a(4)

Simplifying each term:

4a(a2) = 4a3
4a(7a) = 28a2
4a(4) = 16a

So combining the terms, we get:

4a(a2 + 7a + 4) = 4a3 + 28a2 + 16a

Therefore, the answer is B. 4a3 + 28a2 + 16a.
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