Question

What is the product?

Answer 1

Hey there!

In order to solve this problem, you'll look at (x⁴)(3x³ – 2) first. You need to multiply 4x by both numbers in the binomial to get the distributed version that you'll use later on. 

(x⁴)(3x³) = 3x⁷
(x⁴)(–2) = –2x⁴

Now, your problem is (3x⁷ – 2x⁴)(4x² + 5x). You will complete the distributing by multiplying the first term of the first binomial by both terms of the second binomial, then repeating this with the second term. You'll then want to add or subtract any repeated terms to combine them, if applicable. Remember that to multiply exponents together, all you need to do is add the numbers. x is the same as x¹.

(3x⁷)(4x²) = 12x⁹
(3x⁷)(5x) = 15x⁸
(–2x⁴)(4x²) = –8x⁶
(–2x⁴)(5x) = –10x⁵

So, your final expanded product will be (12x⁹ + 15x⁸ – 8x⁶ – 10x⁵). Your answer should be letter A. Hope this helped you out! :-)