Question

Which expression is equivalent to (x2 – 3x)(4x2 + 2x – 9)?

A. x2(4x2 + 2x – 9) – 3x
B. x2(4x2 + 2x – 9) – 3x(4x2 + 2x – 9)
C. x2(4x2 + 2x – 9) + 3x(4x2 + 2x – 9)
D. x2(4x2 + 2x) – 3x(2x – 9)

Answer 1

That would be  choice B.

Answer 2

B.
`x^2(4x^2 + 2x -9) -3x(4x^2 + 2x - 9)`

Explanation:

The distributivity establish that in order to multiply these two polynomials, first you have to multiply
`x^2` by every element in
`4x^2 + 2x - 9` and then multiply
`-3x` by every element in
`4x^2 + 2x - 9` as well.

That is exactly what the option B. says, since

in the expresion
`x^2(4x^2 + 2x - 9) - 3x(4x^2 + 2x - 9)`
`x^2` is being multiplied by every element in
`(4x^2 + 2x - 9)` and also
`-3x` is being multiplied by every element in
`(4x^2 + 2x - 9)`.