Question

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

Answer 1

To find an expression equivalent to \((2x^2 + 4x - 7)(x - 3)\), we can use the distributive property (also known as the FOIL method for binomials). We will distribute each term in the first polynomial by each term in the second polynomial.

1. Distributing \(2x^2\):
- \(2x^2 \cdot x = 2x^3\)
- \(2x^2 \cdot (-3) = -6x^2\)

2. Distributing \(4x\):
- \(4x \cdot x = 4x^2\)
- \(4x \cdot (-3) = -12x\)

3. Distributing \(-7\):
- \(-7 \cdot x = -7x\)
- \(-7 \cdot (-3) = 21\)

Now, combine all the results:
\[
2x^3 - 6x^2 + 4x^2 - 12x - 7x + 21
\]

Now combine like terms:
- The \(x^2\) terms: \(-6x^2 + 4x^2 = -2x^2\)
- The \(x\) terms: \(-12x - 7x = -19x\)

So the combined expression is:
\[
2x^3 - 2x^2 - 19x + 21
\]

Thus, the expression equivalent to \((2x^2 + 4x - 7)(x - 3)\) is:
\[
\boxed{2x^3 - 2x^2 - 19x + 21}
\]