Algebra Examples

9 x^{2} - 49

$9 x^{2} - 49$

Step 1

Rewrite

9 x^{2}

$9 x^{2}$ as

{(3 x)}^{2}

${(3 x)}^{2}$ .

{(3 x)}^{2} - 49

${(3 x)}^{2} - 49$

Step 2

Rewrite

49

$49$ as

7^{2}

$7^{2}$ .

{(3 x)}^{2} - 7^{2}

${(3 x)}^{2} - 7^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = 3 x

$a = 3 x$ and

b = 7

$b = 7$ .

(3 x + 7) (3 x - 7)

$(3 x + 7) (3 x - 7)$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$