x^5y^2(-5x^4y^3)
Understand the Problem
The question involves multiplying polynomials, specifically the expression x^5y^2 multiplied by -5x^4y^3. We'll combine the terms by applying the distributive property and simplifying the result.
Answer
The solution to the multiplication is $-5x^9y^5$.
Answer for screen readers
The final result is:
$$ -5x^9y^5 $$
Steps to Solve
- Identify the expression to multiply
We need to multiply the two polynomial expressions:
$$ x^5y^2 \cdot (-5x^4y^3) $$
- Multiply the coefficients
We start by multiplying the numerical coefficients. Since there is no coefficient in $x^5y^2$, we assume it has a coefficient of 1:
$$ 1 \cdot (-5) = -5 $$
- Multiply the $x$ terms
Next, we multiply the $x$ terms. We apply the property of exponents, which states that ( x^a \cdot x^b = x^{a+b} ):
$$ x^5 \cdot x^4 = x^{5+4} = x^9 $$
- Multiply the $y$ terms
Now, we do the same for the $y$ terms:
$$ y^2 \cdot y^3 = y^{2+3} = y^5 $$
- Combine the results
Now, we combine all the parts we have calculated:
$$ -5x^9y^5 $$
The final result is:
$$ -5x^9y^5 $$
More Information
This result combines the coefficients and adds the exponents according to the rules of exponents for multiplying polynomials. Knowing how to handle the multiplicative properties of exponents is essential when working with polynomials.
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