Factor completely. 45x^(5)y^(6)+27x^(4)y^(4)z^(3) Answer:

Identify GCF: Identify the greatest common factor (GCF) of the two terms. The GCF of 45 and 27 is 9. The GCF of x^(5) and x^(4) is x^(4). The GCF of y^(6) and y^(4) is y^(4). There is no z term in the first expression, so z^(3) is not part of the GCF.Factor out GCF: Factor out the GCF from the original expression. The GCF is 9x^(4)y^(4), so we factor this out from each term. 45x^(5)y^(6)+27x^(4)y^(4)z^(3) = 9x^(4)y^(4)(5x^(5-4)y^(6-4) + 3z^(3))Simplify inside parentheses: Simplify the expression inside the parentheses. Subtract the exponents for x and y in the first term inside the parentheses since we factored out x^(4) and y^(4). 5x^(5-4)y^(6-4) + 3z^(3) = 5x^(1)y^(2) + 3z^(3)Write final factored expression: Write the final factored expression. The completely factored form is 9x^(4)y^(4)(5xy^(2) + 3z^(3)).

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Q. Factor completely.

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45 x^{5} y^{6}+27 x^{4} y^{4} z^{3}

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Answer:

Identify GCF: Identify the greatest common factor (GCF) of the two terms. $\newline$ The GCF of $45$ and $27$ is $9$ . The GCF of $x^{5}$ and $x^{4}$ is $x^{4}$ . The GCF of $y^{6}$ and $y^{4}$ is $y^{4}$ . There is no $z$ term in the first expression, so $27$ $0$ is not part of the GCF.
Factor out GCF: Factor out the GCF from the original expression. $\newline$ The GCF is $9x^{4}y^{4}$ , so we factor this out from each term. $\newline$ $45x^{5}y^{6}+27x^{4}y^{4}z^{3} = 9x^{4}y^{4}(5x^{5-4}y^{6-4} + 3z^{3})$
Simplify inside parentheses: Simplify the expression inside the parentheses. $\newline$ Subtract the exponents for $x$ and $y$ in the first term inside the parentheses since we factored out $x^{4}$ and $y^{4}$ . $\newline$ $5x^{(5-4)}y^{(6-4)} + 3z^{3} = 5x^{1}y^{2} + 3z^{3}$
Write final factored expression: Write the final factored expression. $\newline$ The completely factored form is $9x^{4}y^{4}(5xy^{2} + 3z^{3})$ .