Factor completely. 25x^(2)-16=

Identify Expression Type: Step Title: Identify the Type of Expression Concise Step Description: Recognize that the given expression is a difference of squares. Calculation: The expression 25x^2 - 16 can be written as (5x)^2 - 4^2, which is a difference of squares since both 25x^2 and 16 are perfect squares.Apply Formula: Step Title: Apply the Difference of Squares Formula Concise Step Description: Use the difference of squares formula, which is a^2 - b^2 = (a + b)(a - b), to factor the expression. Calculation: Let a = 5x and b = 4. Then, the factored form is (5x + 4)(5x - 4).Write Final Form: Step Title: Write the Final Factored Form Concise Step Description: Write down the final factored form of the expression. Calculation: The final factored form is (5x + 4)(5x - 4).

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

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25x^{2}-16

Identify Expression Type: Step Title: Identify the Type of Expression $\newline$ Concise Step Description: Recognize that the given expression is a difference of squares. $\newline$ Calculation: The expression $25x^2 - 16$ can be written as $(5x)^2 - 4^2$ , which is a difference of squares since both $25x^2$ and $16$ are perfect squares.
Apply Formula: Step Title: Apply the Difference of Squares Formula $\newline$ Concise Step Description: Use the difference of squares formula, which is $a^2 - b^2 = (a + b)(a - b)$ , to factor the expression. $\newline$ Calculation: Let $a = 5x$ and $b = 4$ . Then, the factored form is $(5x + 4)(5x - 4)$ .
Write Final Form: Step Title: Write the Final Factored Form $\newline$ Concise Step Description: Write down the final factored form of the expression. $\newline$ Calculation: The final factored form is $(5x + 4)(5x - 4)$ .