Factor the expression completely. x^(5)y^(2)-x^(3)y^(5) Answer:

Identify common factors: Identify the common factors in both terms. We have the expression x^(5)y^(2) - x^(3)y^(5). To factor it completely, we need to find the greatest common factor (GCF) of the two terms. The GCF is the highest power of x and y that is present in both terms.Determine GCF: Determine the GCF of the two terms. The GCF of x^(5)y^(2) and x^(3)y^(5) is x^(3)y^(2), because x^(3) is the highest power of x that is present in both terms, and y^(2) is the highest power of y that is present in both terms.Factor out GCF: Factor out the GCF from the expression. We can write the original expression as the GCF multiplied by what is left after dividing each term by the GCF. x^(5)y^(2) - x^(3)y^(5) = x^(3)y^(2)(x^(5-3)y^(2-2) - x^(3-3)y^(5-2))Simplify expression: Simplify the expression inside the parentheses. Subtract the exponents inside the parentheses, as we have factored out the common factors. x^(3)y^(2)(x^(2)y^(0) - x^(0)y^(3)) Since any number raised to the power of 0 is 1, we have: x^(3)y^(2)(x^(2)*1 - 1*y^(3)) This simplifies to: x^(3)y^(2)(x^(2) - y^(3))Write final factored expression: Write the final factored expression. The completely factored form of the expression is: x^(3)y^(2)(x^(2) - y^(3))

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Factor the expression completely.

x^(5)y^(2)-x^(3)y^(5)
Answer:

Factor the expression completely. $\newline$ $x^{5} y^{2}-x^{3} y^{5}$ $\newline$ Answer:

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Algebra 1

Multiplication with rational exponents

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Q. Factor the expression completely.

\newline

x^{5} y^{2}-x^{3} y^{5}

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Answer:

Identify common factors: Identify the common factors in both terms. $\newline$ We have the expression $x^{5}y^{2} - x^{3}y^{5}$ . To factor it completely, we need to find the greatest common factor (GCF) of the two terms. The GCF is the highest power of $x$ and $y$ that is present in both terms.
Determine GCF: Determine the GCF of the two terms. $\newline$ The GCF of $x^{5}y^{2}$ and $x^{3}y^{5}$ is $x^{3}y^{2}$ , because $x^{3}$ is the highest power of $x$ that is present in both terms, and $y^{2}$ is the highest power of $y$ that is present in both terms.
Factor out GCF: Factor out the GCF from the expression. $\newline$ We can write the original expression as the GCF multiplied by what is left after dividing each term by the GCF. $\newline$ $x^{5}y^{2} - x^{3}y^{5} = x^{3}y^{2}(x^{5-3}y^{2-2} - x^{3-3}y^{5-2})$
Simplify expression: Simplify the expression inside the parentheses. $\newline$ Subtract the exponents inside the parentheses, as we have factored out the common factors. $\newline$ $x^{3}y^{2}(x^{2}y^{0} - x^{0}y^{3})$ $\newline$ Since any number raised to the power of $0$ is $1$ , we have: $\newline$ $x^{3}y^{2}(x^{2}\cdot 1 - 1\cdot y^{3})$ $\newline$ This simplifies to: $\newline$ $x^{3}y^{2}(x^{2} - y^{3})$
Write final factored expression: Write the final factored expression. $\newline$ The completely factored form of the expression is: $\newline$ $x^{3}y^{2}(x^{2} - y^{3})$