Question

Which expression is equivalent to (x^2 - 3x) (4x^2 + 2x-9)?

A. x^2 (4x^2 + 2x - 9) -3x
B. x^2 (4x^2 + 2x)-3x(2x-9)
C.x^2(4x^2 + 2x -9)+3x(4x^2 + 2x - 9)
D. x^2 (4x^2 + 2x - 9) - 3x (4x^2 + 2x - 9)

Answer 1

To find the expression equivalent to \((x^2 - 3x) (4x^2 + 2x - 9)\), we can factor the expression \((x^2 - 3x)\) and distribute it across the expression \((4x^2 + 2x - 9)\).

The expression can be rewritten by factoring out \((4x^2 + 2x - 9)\):

\[
(x^2 - 3x)(4x^2 + 2x - 9) = x^2(4x^2 + 2x - 9) - 3x(4x^2 + 2x - 9)
\]

Now, compare this with the options provided:

- **A.** \(x^2 (4x^2 + 2x - 9) - 3x\) (This is incorrect because it doesn't account for the full term \((4x^2 + 2x - 9)\))
- **B.** \(x^2 (4x^2 + 2x) - 3x(2x - 9)\) (This is incorrect because it's not factoring out the whole \((4x^2 + 2x - 9)\))
- **C.** \(x^2(4x^2 + 2x - 9) + 3x(4x^2 + 2x - 9)\) (This is incorrect because it's an addition instead of subtraction)
- **D.** \(x^2 (4x^2 + 2x - 9) - 3x (4x^2 + 2x - 9)\) (This is correct and has the correct distribution)

Thus, the correct choice is:

**D.** \(x^2 (4x^2 + 2x - 9) - 3x (4x^2 + 2x - 9)\)