Factor. 16x^2 - 25 ______

Recognize Difference of Squares: Determine the approach to factor 16x^2 - 25. We can recognize this expression as a difference of squares because it is in the form a^2 - b^2, where both 16x^2 and 25 are perfect squares.Identify Square Roots: Identify the square roots of each term in the expression. The square root of 16x^2 is 4x, since (4x)^2 = 16x^2. The square root of 25 is 5, since 5^2 = 25.Apply Formula: Apply the difference of squares formula. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). Here, a = 4x and b = 5, so we have: (4x)^2 - 5^2 = (4x - 5)(4x + 5).Write Factored Form: Write the final factored form. The factored form of 16x^2 - 25 is (4x - 5)(4x + 5).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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16x^2 - 25

Recognize Difference of Squares: Determine the approach to factor $16x^2 - 25$ . We can recognize this expression as a difference of squares because it is in the form $a^2 - b^2$ , where both $16x^2$ and $25$ are perfect squares.
Identify Square Roots: Identify the square roots of each term in the expression. $\newline$ The square root of $16x^2$ is $4x$ , since $(4x)^2 = 16x^2$ . $\newline$ The square root of $25$ is $5$ , since $5^2 = 25$ .
Apply Formula: Apply the difference of squares formula. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ Here, $a = 4x$ and $b = 5$ , so we have: $\newline$ $(4x)^2 - 5^2 = (4x - 5)(4x + 5)$ .
Write Factored Form: Write the final factored form. $\newline$ The factored form of $16x^2 - 25$ is $(4x - 5)(4x + 5)$ .