Factor. 25m^2 - 16 ______

Recognize as Difference of Squares: Determine the approach to factor 25m^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 25m^2 - 16. 25m^2 can be written as (5m)^2 because 5m * 5m = 25m^2. 16 can be written as 4^2 because 4 * 4 = 16. So, 25m^2 - 16 can be rewritten as (5m)^2 - 4^2.Apply Difference of Squares Formula: 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 factor (5m)^2 - 4^2 as (5m - 4)(5m + 4).

Home

Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor.

\newline

25m^2 - 16

Recognize as Difference of Squares: Determine the approach to factor $25m^2 - 16$ . 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 $25m^2 - 16$ . $25m^2$ can be written as $(5m)^2$ because $5m \times 5m = 25m^2$ . $16$ can be written as $4^2$ because $4 \times 4 = 16$ . So, $25m^2 - 16$ can be rewritten as $(5m)^2 - 4^2$ .
Apply Difference of Squares Formula: 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 factor $(5m)^2 - 4^2$ as $(5m - 4)(5m + 4)$ .