Factor completely: 4x^(2)(x^(2)-7)-25(x^(2)-7) Answer:

Identify Common Factor: Identify the common factor in both terms of the expression. The common factor is (x^(2)-7).Factor Out Common Factor: Factor out the common factor from the expression. 4x^(2)(x^(2)-7)-25(x^(2)-7) = (x^(2)-7)(4x^(2)-25)Recognize Difference of Squares: Recognize that the expression inside the parentheses is a difference of squares. 4x^(2)-25 can be factored as (2x)^2 - (5)^2, which is a difference of squares.Apply Factoring Formula: Apply the difference of squares factoring formula: a^2 - b^2 = (a+b)(a-b). (4x^(2)-25) = (2x+5)(2x-5)Combine Factored Parts: Combine the factored parts to write the final factored form of the original expression. (4x^(2)(x^(2)-7)-25(x^(2)-7)) = (x^(2)-7)(2x+5)(2x-5)

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Q. Factor completely:

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4 x^{2}\left(x^{2}-7\right)-25\left(x^{2}-7\right)

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Answer:

Identify Common Factor: Identify the common factor in both terms of the expression. $\newline$ The common factor is $x^{2}-7$ .
Factor Out Common Factor: Factor out the common factor from the expression. $\newline$ $4x^{2}(x^{2}-7)-25(x^{2}-7) = (x^{2}-7)(4x^{2}-25)$
Recognize Difference of Squares: Recognize that the expression inside the parentheses is a difference of squares. $4x^{2}-25$ can be factored as $(2x)^2 - (5)^2$ , which is a difference of squares.
Apply Factoring Formula: Apply the difference of squares factoring formula: $a^2 - b^2 = (a+b)(a-b)$ .
$(4x^{2}-25) = (2x+5)(2x-5)$
Combine Factored Parts: Combine the factored parts to write the final factored form of the original expression. $\newline$ $(4x^{2}(x^{2}-7)-25(x^{2}-7)) = (x^{2}-7)(2x+5)(2x-5)$