Factor completely. 24x^(6)y^(2)z^(3)-42x^(4)y^(4)z^(6) Answer:

Identify GCF: Identify the greatest common factor (GCF) of the two terms. Calculation: The GCF of 24 and 42 is 6. The GCF of x^(6) and x^(4) is x^(4). The GCF of y^(2) and y^(4) is y^(2). The GCF of z^(3) and z^(6) is z^(3). GCF = 6x^(4)y^(2)z^(3)Factor Out GCF: Factor out the GCF from the original expression. Calculation: 24x^(6)y^(2)z^(3) - 42x^(4)y^(4)z^(6) = 6x^(4)y^(2)z^(3)(4x^(6-4)y^(2-2)z^(3-3) - 7x^(4-4)y^(4-2)z^(6-3)) = 6x^(4)y^(2)z^(3)(4x^(2) - 7y^(2)z^(3))Check Factored Expression: Check the factored expression to ensure it is equivalent to the original expression when multiplied out. Calculation: 6x^(4)y^(2)z^(3)(4x^(2) - 7y^(2)z^(3)) = 24x^(6)y^(2)z^(3) - 42x^(4)y^(4)z^(6) This matches the original expression.

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Q. Factor completely.

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24 x^{6} y^{2} z^{3}-42 x^{4} y^{4} z^{6}

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Answer:

Identify GCF: Identify the greatest common factor (GCF) of the two terms. $\newline$ Calculation: The GCF of $24$ and $42$ is $6$ . The GCF of $x^{6}$ and $x^{4}$ is $x^{4}$ . The GCF of $y^{2}$ and $y^{4}$ is $y^{2}$ . The GCF of $z^{3}$ and $42$ $0$ is $z^{3}$ . $\newline$ GCF = $42$ $2$
Factor Out GCF: Factor out the GCF from the original expression. $\newline$ Calculation: $\newline$ $24x^{6}y^{2}z^{3} - 42x^{4}y^{4}z^{6} = 6x^{4}y^{2}z^{3}(4x^{6-4}y^{2-2}z^{3-3} - 7x^{4-4}y^{4-2}z^{6-3})$ $\newline$ $= 6x^{4}y^{2}z^{3}(4x^{2} - 7y^{2}z^{3})$
Check Factored Expression: Check the factored expression to ensure it is equivalent to the original expression when multiplied out. $\newline$ Calculation: $\newline$ $6x^{4}y^{2}z^{3}(4x^{2} - 7y^{2}z^{3}) = 24x^{6}y^{2}z^{3} - 42x^{4}y^{4}z^{6}$ $\newline$ This matches the original expression.