Factor completely: 25x^(2)(2x^(2)-5)-16(2x^(2)-5) Answer:

Identify Common Factor: Identify the common factor in both terms of the expression. The common factor is (2x^(2) - 5).Factor Out Common Factor: Factor out the common factor (2x^(2) - 5) from both terms. The expression becomes (2x^(2) - 5)(25x^(2) - 16).Recognize Perfect Squares: Recognize that both 25x^(2) and 16 are perfect squares. 25x^(2) is the square of 5x, and 16 is the square of 4.Write as Difference of Squares: Write the second term as a difference of squares. The expression (25x^(2) - 16) can be written as (5x - 4)(5x + 4).Combine Factored Expressions: Combine the factored common factor with the difference of squares. The completely factored expression is (2x^(2) - 5)(5x - 4)(5x + 4).

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Factor completely:

25x^(2)(2x^(2)-5)-16(2x^(2)-5)
Answer:

Factor completely: $\newline$ $25 x^{2}\left(2 x^{2}-5\right)-16\left(2 x^{2}-5\right)$ $\newline$ Answer:

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Precalculus

Operations with rational exponents

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Q. Factor completely:

\newline

25 x^{2}\left(2 x^{2}-5\right)-16\left(2 x^{2}-5\right)

\newline

Answer:

Identify Common Factor: Identify the common factor in both terms of the expression. $\newline$ The common factor is $(2x^{2} - 5)$ .
Factor Out Common Factor: Factor out the common factor $(2x^{2} - 5)$ from both terms. $\newline$ The expression becomes $(2x^{2} - 5)(25x^{2} - 16)$ .
Recognize Perfect Squares: Recognize that both $25x^{2}$ and $16$ are perfect squares. $\newline$ $25x^{2}$ is the square of $5x$ , and $16$ is the square of $4$ .
Write as Difference of Squares: Write the second term as a difference of squares. $\newline$ The expression $(25x^{2} - 16)$ can be written as $(5x - 4)(5x + 4)$ .
Combine Factored Expressions: Combine the factored common factor with the difference of squares. $\newline$ The completely factored expression is $(2x^{2} - 5)(5x - 4)(5x + 4)$ .