Factor completely. 3x^(5)-75x^(3)=

Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression. The terms 3x^(5) and 75x^(3) both have a common factor of 3x^(3).Factor out GCF: Factor out the GCF from the expression. The expression 3x^(5) - 75x^(3) can be factored as 3x^(3)(x^(2) - 25).Recognize difference of squares: Recognize that the expression inside the parentheses is a difference of squares. The expression x^(2) - 25 can be factored further because it is a difference of squares, where x^(2) is the square of x and 25 is the square of 5.Factor difference of squares: Factor the difference of squares. The expression x^(2) - 25 can be factored into (x + 5)(x - 5).Write final factored form: Write the final factored form of the original expression. Combining the GCF factored out in Step 2 with the factored form of the difference of squares from Step 4, we get the final factored form: 3x^(3)(x + 5)(x - 5).

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Factor completely. $\newline$ $3 x^{5}-75 x^{3}=$

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Math Problems

Grade 8

Powers with negative bases

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Q. Factor completely.

\newline

3 x^{5}-75 x^{3}=

Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression. $\newline$ The terms $3x^{5}$ and $75x^{3}$ both have a common factor of $3x^{3}$ .
Factor out GCF: Factor out the GCF from the expression. $\newline$ The expression $3x^{5} - 75x^{3}$ can be factored as $3x^{3}(x^{2} - 25)$ .
Recognize difference of squares: Recognize that the expression inside the parentheses is a difference of squares. The expression $x^{2} - 25$ can be factored further because it is a difference of squares, where $x^{2}$ is the square of $x$ and $25$ is the square of $5$ .
Factor difference of squares: Factor the difference of squares. $\newline$ The expression $x^{2} - 25$ can be factored into $(x + 5)(x - 5)$ .
Write final factored form: Write the final factored form of the original expression. Combining the GCF factored out in Step $2$ with the factored form of the difference of squares from Step $4$ , we get the final factored form: $3x^{3}(x + 5)(x - 5)$ .