Factor. 9c^2 - 16 ______

Identify Factoring Technique: Determine the appropriate factoring technique for 9c^2 - 16. The expression is a difference of squares because it can be written as a^2 - b^2, where both terms are perfect squares.Identify Squares: Identify the squares in the expression 9c^2 - 16. 9c^2 can be written as (3c)^2 because 3c * 3c = 9c^2. 16 can be written as 4^2 because 4 * 4 = 16. So, 9c^2 - 16 is equivalent to (3c)^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 write (3c)^2 - 4^2 as (3c - 4)(3c + 4).

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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9c^2 - 16

Identify Factoring Technique: Determine the appropriate factoring technique for $9c^2 - 16$ . The expression is a difference of squares because it can be written as $a^2 - b^2$ , where both terms are perfect squares.
Identify Squares: Identify the squares in the expression $9c^2 - 16$ . $9c^2$ can be written as $(3c)^2$ because $3c \times 3c = 9c^2$ . $16$ can be written as $4^2$ because $4 \times 4 = 16$ . So, $9c^2 - 16$ is equivalent to $(3c)^2 - 4^2$ .
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 write $(3c)^2 - 4^2$ as $(3c - 4)(3c + 4)$ .