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Factor. $\newline$ $16x^2 - 9$

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Factor quadratics: special cases

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Q. Factor.

\newline

16x^2 - 9

Identify method for factoring: Determine the appropriate method to factor $16x^2 - 9$ . We can observe that the expression is a difference of squares because it is in the form of $a^2 - b^2$ , where $16x^2$ is a perfect square and $9$ is also a perfect square.
Express as difference of squares: Express $16x^2 - 9$ as a difference of squares. $\newline$ $16x^2$ can be written as $(4x)^2$ because $4x \times 4x = 16x^2$ . $\newline$ $9$ can be written as $3^2$ because $3 \times 3 = 9$ . $\newline$ So, $16x^2 - 9$ can be rewritten as $(4x)^2 - 3^2$ .
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 $(4x)^2 - 3^2$ as $(4x - 3)(4x + 3)$ .

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