Questions: What is the product of 5x^3 and xy^4-2x^3y? 5x^3y^4-10x^6y 5x^4y^4-10x^9y 5x^4y^4-10x^6y 5x^3y^4-10x^9y

What is the product of 5x^3 and xy^4-2x^3y? 5x^3y^4-10x^6y 5x^4y^4-10x^9y 5x^4y^4-10x^6y 5x^3y^4-10x^9y
Transcript text: What is the product of $5 x^{3}$ and $x y^{4}-2 x^{3} y$ ? $5 x^{3} y^{4}-10 x^{6} y$ $5 x^{4} y^{4}-10 x^{9} y$ $5 x^{4} y^{4}-10 x^{6} y$ $5 x^{3} y^{4}-10 x^{9} y$
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Solution

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Solution Steps

To find the product of \(5x^3\) and \(xy^4 - 2x^3y\), we need to distribute \(5x^3\) to each term inside the parentheses. This involves multiplying the coefficients and adding the exponents of like bases according to the laws of exponents.

Step 1: Distribute \(5x^3\) to Each Term

To find the product of \(5x^3\) and \(xy^4 - 2x^3y\), we distribute \(5x^3\) to each term inside the parentheses:

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

  2. Multiply \(5x^3\) by \(-2x^3y\): \[ 5x^3 \cdot (-2x^3y) = -10x^{3+3}y = -10x^6y \]

Step 2: Combine the Results

Combine the results from the distribution:

\[ 5x^4y^4 - 10x^6y \]

Final Answer

The product of \(5x^3\) and \(xy^4 - 2x^3y\) is:

\[ \boxed{5x^4y^4 - 10x^6y} \]

For the multiple-choice question, the correct answer is \(5x^4y^4 - 10x^6y\), which corresponds to option C.

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