Question

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

Answer 1

To find an expression equivalent to \((x^2-2x)(3x^2+4x-7)\), we can use the distributive property (also known as the FOIL method for binomials, but applied here to a binomial multiplied by a trinomial).

Let's expand the expression step by step:

1. Distribute \(x^2\) to each term in \(3x^2 + 4x - 7\):
\[
x^2 \cdot 3x^2 = 3x^4
\]
\[
x^2 \cdot 4x = 4x^3
\]
\[
x^2 \cdot (-7) = -7x^2
\]

2. Next, distribute \(-2x\) to each term in \(3x^2 + 4x - 7\):
\[
-2x \cdot 3x^2 = -6x^3
\]
\[
-2x \cdot 4x = -8x^2
\]
\[
-2x \cdot (-7) = 14x
\]

3. Now, combine all the terms:
\[
3x^4 + 4x^3 - 7x^2 - 6x^3 - 8x^2 + 14x
\]

4. Combine like terms:
- For \(x^3\): \(4x^3 - 6x^3 = -2x^3\)
- For \(x^2\): \(-7x^2 - 8x^2 = -15x^2\)
- For \(x\): \(14x\) remains as is.

Putting it all together, we have:
\[
3x^4 - 2x^3 - 15x^2 + 14x
\]

So, the expression equivalent to \((x^2-2x)(3x^2+4x-7)\) is:
\[
3x^4 - 2x^3 - 15x^2 + 14x
\]