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

Identify GCF: We need to factor the expression x^(5)y^(5) + x^(3)y^(3). To do this, we look for the greatest common factor (GCF) of the two terms. The GCF of x^(5)y^(5) and x^(3)y^(3) is x^(3)y^(3), because that is the highest power of both x and y that divides into both terms.Factor out GCF: Now we factor out the GCF from each term in the expression. x^(5)y^(5) + x^(3)y^(3) = x^(3)y^(3)(x^(5-3)y^(5-3)) + x^(3)y^(3)(1)Simplify expression: Simplify the expression inside the parentheses. x^(3)y^(3)(x^(2)y^(2)) + x^(3)y^(3)(1) = x^(3)y^(3)(x^(2)y^(2) + 1)Final factored form: We have now factored the expression completely. There are no common factors in the term x^(2)y^(2) + 1, so we cannot factor further. The completely factored form of the expression is x^(3)y^(3)(x^(2)y^(2) + 1).

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Q. Factor the expression completely.

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x^{5} y^{5}+x^{3} y^{3}

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Answer:

Identify GCF: We need to factor the expression $x^{5}y^{5} + x^{3}y^{3}$ . To do this, we look for the greatest common factor (GCF) of the two terms. $\newline$ The GCF of $x^{5}y^{5}$ and $x^{3}y^{3}$ is $x^{3}y^{3}$ , because that is the highest power of both $x$ and $y$ that divides into both terms.
Factor out GCF: Now we factor out the GCF from each term in the expression. $x^{5}y^{5} + x^{3}y^{3} = x^{3}y^{3}(x^{5-3}y^{5-3}) + x^{3}y^{3}(1)$
Simplify expression: Simplify the expression inside the parentheses. $x^{3}y^{3}(x^{2}y^{2}) + x^{3}y^{3}(1) = x^{3}y^{3}(x^{2}y^{2} + 1)$
Final factored form: We have now factored the expression completely. There are no common factors in the term $x^{2}y^{2} + 1$ , so we cannot factor further. $\newline$ The completely factored form of the expression is $x^{3}y^{3}(x^{2}y^{2} + 1)$ .