Question

Find the product when you multiply the polynomials (−4x4+10x)(5x3−1) .

−20x7+50x4−6x
negative 20 x superscript 7 baseline plus 50 x superscript 4 baseline minus 6 x

−20x7−54x4−10x
negative 20 x superscript 7 baseline minus 54 x superscript 4 baseline minus 10 x

−20x7+54x4−10x
negative 20 x superscript 7 baseline plus 54 x superscript 4 baseline minus 10 x

20x7+54x4−10x

Answer 1

To find the product of the polynomials \((-4x^4 + 10x)(5x^3 - 1)\), we will apply the distributive property (also known as the FOIL method for binomials) by multiplying each term in the first polynomial by each term in the second polynomial.

1. **Multiply \(-4x^4\) by \(5x^3\)**:
\[
-4x^4 \cdot 5x^3 = -20x^{4+3} = -20x^7
\]

2. **Multiply \(-4x^4\) by \(-1\)**:
\[
-4x^4 \cdot -1 = 4x^4
\]

3. **Multiply \(10x\) by \(5x^3\)**:
\[
10x \cdot 5x^3 = 50x^{1+3} = 50x^4
\]

4. **Multiply \(10x\) by \(-1\)**:
\[
10x \cdot -1 = -10x
\]

Now, we can combine all of these results:
\[
-20x^7 + 4x^4 + 50x^4 - 10x
\]

Next, we combine like terms \(4x^4\) and \(50x^4\):
\[
4x^4 + 50x^4 = 54x^4
\]

Putting it all together, we have:
\[
-20x^7 + 54x^4 - 10x
\]

Thus, the product of the polynomials \((-4x^4 + 10x)(5x^3 - 1)\) is:
\[
\boxed{-20x^7 + 54x^4 - 10x}
\]