Factor completely. -18x^(5)y^(4)z^(4)-13x^(2)y^(2)z^(5) Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression. -18x^(5)y^(4)z^(4) and -13x^(2)y^(2)z^(5) share a common factor of x^(2)y^(2)z^(4).Factor out GCF: Factor out the GCF from each term in the expression. GCF * (Term1/GCF + Term2/GCF) = x^(2)y^(2)z^(4) * (-18x^(5)y^(4)z^(4)/x^(2)y^(2)z^(4) - 13x^(2)y^(2)z^(5)/x^(2)y^(2)z^(4))Simplify expression: Simplify the expression inside the parentheses. -18x^(5)y^(4)z^(4)/x^(2)y^(2)z^(4) = -18x^(3)y^(2) -13x^(2)y^(2)z^(5)/x^(2)y^(2)z^(4) = -13z So, the factored expression is x^(2)y^(2)z^(4) * (-18x^(3)y^(2) - 13z)Combine terms: Combine the GCF and the simplified terms to write the final factored expression. The completely factored form is -x^(2)y^(2)z^(4)(18x^(3)y^(2) + 13z).

Home

Math Problems

Calculus

Find derivatives of using multiple formulae

Full solution

Q. Factor completely.

\newline

-18 x^{5} y^{4} z^{4}-13 x^{2} y^{2} z^{5}

\newline

Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression. $\newline$ $-18x^{5}y^{4}z^{4}$ and $-13x^{2}y^{2}z^{5}$ share a common factor of $x^{2}y^{2}z^{4}$ .
Factor out GCF: Factor out the GCF from each term in the expression. $\newline$ $\text{GCF} \times (\frac{\text{Term1}}{\text{GCF}} + \frac{\text{Term2}}{\text{GCF}}) = x^{2}y^{2}z^{4} \times (\frac{-18x^{5}y^{4}z^{4}}{x^{2}y^{2}z^{4}} - \frac{13x^{2}y^{2}z^{5}}{x^{2}y^{2}z^{4}})$
Simplify expression: Simplify the expression inside the parentheses. $\newline$ $-18x^{5}y^{4}z^{4}/x^{2}y^{2}z^{4} = -18x^{3}y^{2}$ $\newline$ $-13x^{2}y^{2}z^{5}/x^{2}y^{2}z^{4} = -13z$ $\newline$ So, the factored expression is $x^{2}y^{2}z^{4} * (-18x^{3}y^{2} - 13z)$
Combine terms: Combine the GCF and the simplified terms to write the final factored expression. $\newline$ The completely factored form is $-x^{2}y^{2}z^{4}(18x^{3}y^{2} + 13z)$ .