Question

Factor 9x^2 -5 . using difference of squares

Answer 1

$\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------\\\\ 9x^2-5\qquad \begin{cases} 9x^2=3^2x^2\\ \qquad (3x)^2\\ 5=\sqrt{5^2}\\ \qquad (\sqrt{5})^2 \end{cases}\implies \begin{array}{llll} (3x)^2-(\sqrt{5})^2 \\\\\\ (3x-\sqrt{5})~(3x+\sqrt{5}) \end{array}$