Asked by jim
Find the product when you multiply the polynomials (−4x4+10x)(5x3−1) .
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Answered by
GPT-4o mini
To find the product of the polynomials \((-4x^4 + 10x)(5x^3 - 1)\), we can use the distributive property (also known as the FOIL method for binomials).
We will distribute each term in the first polynomial \((-4x^4 + 10x)\) with each term in the second polynomial \((5x^3 - 1)\):
1. \( -4x^4 \times 5x^3 = -20x^7 \)
2. \( -4x^4 \times (-1) = 4x^4 \)
3. \( 10x \times 5x^3 = 50x^4 \)
4. \( 10x \times (-1) = -10x \)
Now, we combine all these results:
\[
-20x^7 + 4x^4 + 50x^4 - 10x
\]
Next, we combine like terms:
\[
-20x^7 + (4x^4 + 50x^4) - 10x = -20x^7 + 54x^4 - 10x
\]
So, the product of the polynomials \((-4x^4 + 10x)(5x^3 - 1)\) is:
\[
\boxed{-20x^7 + 54x^4 - 10x}
\]
We will distribute each term in the first polynomial \((-4x^4 + 10x)\) with each term in the second polynomial \((5x^3 - 1)\):
1. \( -4x^4 \times 5x^3 = -20x^7 \)
2. \( -4x^4 \times (-1) = 4x^4 \)
3. \( 10x \times 5x^3 = 50x^4 \)
4. \( 10x \times (-1) = -10x \)
Now, we combine all these results:
\[
-20x^7 + 4x^4 + 50x^4 - 10x
\]
Next, we combine like terms:
\[
-20x^7 + (4x^4 + 50x^4) - 10x = -20x^7 + 54x^4 - 10x
\]
So, the product of the polynomials \((-4x^4 + 10x)(5x^3 - 1)\) is:
\[
\boxed{-20x^7 + 54x^4 - 10x}
\]
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