Factor. 25w^2 - 16 ______

Recognize as Difference of Squares: Determine the approach to factor 25w^2 - 16. We can recognize this expression as a difference of squares because it is in the form a^2 - b^2, where both terms are perfect squares.Identify Perfect Squares: Identify the squares in the expression 25w^2 - 16. 25w^2 can be written as (5w)^2 because 5w * 5w = 25w^2. 16 can be written as 4^2 because 4 * 4 = 16. So, 25w^2 - 16 can be expressed as (5w)^2 - 4^2.Apply Formula to Factor: Apply the difference of squares formula to factor the expression. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). Using this formula, we can write (5w)^2 - 4^2 as (5w - 4)(5w + 4).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25w^2 - 16

Recognize as Difference of Squares: Determine the approach to factor $25w^2 - 16$ . We can recognize this expression as a difference of squares because it is in the form $a^2 - b^2$ , where both terms are perfect squares.
Identify Perfect Squares: Identify the squares in the expression $25w^2 - 16$ . $25w^2$ can be written as $(5w)^2$ because $5w \times 5w = 25w^2$ . $16$ can be written as $4^2$ because $4 \times 4 = 16$ . So, $25w^2 - 16$ can be expressed as $(5w)^2 - 4^2$ .
Apply Formula to Factor: Apply the difference of squares formula to factor the expression. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ Using this formula, we can write $(5w)^2 - 4^2$ as $(5w - 4)(5w + 4)$ .