Factor completely. 48x^(3)z^(4)-44x^(6)yz^(3) Answer:

Identify GCF: Identify the greatest common factor (GCF) of the two terms in the expression 48x^(3)z^(4) and -44x^(6)yz^(3). The GCF is the product of the lowest powers of common factors. Both terms have a common factor of 4, x, and z. The lowest power of x common to both terms is x^(3), and the lowest power of z is z^(3). Calculate the GCF: 4 * x^(3) * z^(3) = 4x^(3)z^(3).Calculate GCF: Factor out the GCF from the original expression. Divide each term by the GCF to find the remaining factors. 48x^(3)z^(4) / 4x^(3)z^(3) = 12z and -44x^(6)yz^(3) / 4x^(3)z^(3) = -11x^(3)y. Write the factored expression as the GCF multiplied by the remaining factors: 4x^(3)z^(3)(12z - 11x^(3)y).Factor out GCF: Check the factored expression to ensure that when it is expanded, it results in the original expression. Multiply the GCF by each term in the parentheses: 4x^(3)z^(3) * 12z = 48x^(3)z^(4) and 4x^(3)z^(3) * -11x^(3)y = -44x^(6)yz^(3). Combine the two products to confirm that they equal the original expression: 48x^(3)z^(4) - 44x^(6)yz^(3).

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Q. Factor completely.

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48 x^{3} z^{4}-44 x^{6} y z^{3}

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Answer:

Identify GCF: Identify the greatest common factor (GCF) of the two terms in the expression $48x^{3}z^{4}$ and $-44x^{6}yz^{3}$ . The GCF is the product of the lowest powers of common factors. Both terms have a common factor of $4$ , $x$ , and $z$ . The lowest power of $x$ common to both terms is $x^{3}$ , and the lowest power of $z$ is $z^{3}$ . Calculate the GCF: $4 \times x^{3} \times z^{3} = 4x^{3}z^{3}$ .
Calculate GCF: Factor out the GCF from the original expression. $\newline$ Divide each term by the GCF to find the remaining factors. $\newline$ $\frac{48x^{3}z^{4}}{4x^{3}z^{3}} = 12z$ and $\frac{-44x^{6}yz^{3}}{4x^{3}z^{3}} = -11x^{3}y$ . $\newline$ Write the factored expression as the GCF multiplied by the remaining factors: $4x^{3}z^{3}(12z - 11x^{3}y)$ .
Factor out GCF: Check the factored expression to ensure that when it is expanded, it results in the original expression. $\newline$ Multiply the GCF by each term in the parentheses: $4x^{3}z^{3} \times 12z = 48x^{3}z^{4}$ and $4x^{3}z^{3} \times -11x^{3}y = -44x^{6}yz^{3}$ . $\newline$ Combine the two products to confirm that they equal the original expression: $48x^{3}z^{4} - 44x^{6}yz^{3}$ .