Question

which expression is equivalent to (x^2-2x)(3x^2+4x-7)

x^2(3x^2+4x)-2x(4x-7)
x^2(3x^2+4x-7)-2x
x^2(3x^2+4x-7)+2x(3x^2+4x-7)
x^2(3x^2+4x-7)-2x(3x^2+4x-7)

Answer 1

To find an expression equivalent to \((x^2-2x)(3x^2+4x-7)\), we can start by factoring out the common terms in the expression.

The given expression can be rewritten as follows:
\[
x^2(3x^2 + 4x - 7) - 2x(3x^2 + 4x - 7)
\]
This formulation utilizes the distributive property where we factor out \((3x^2 + 4x - 7)\).

To see this more clearly:
1. Look at the original expression:
\[
(x^2 - 2x)(3x^2 + 4x - 7)
\]
2. This can be rewritten by distributing \(x^2\) and \(-2x\) across \((3x^2 + 4x - 7)\):
\[
x^2(3x^2 + 4x - 7) - 2x(3x^2 + 4x - 7)
\]

Thus, the correct choice is:
\[
x^2(3x^2 + 4x - 7) - 2x(3x^2 + 4x - 7)
\]
This corresponds to the option:
\[
x^2(3x^2 + 4x - 7) - 2x(3x^2 + 4x - 7)
\]

Therefore, the equivalent expression is:
**x^2(3x^2 + 4x - 7) - 2x(3x^2 + 4x - 7)**.