Basic Math Examples

90 a^{2} - 250

$90 a^{2} - 250$

Step 1

Factor

10

$10$ out of

90 a^{2} - 250

$90 a^{2} - 250$ .

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Step 1.1

Factor

10

$10$ out of

90 a^{2}

$90 a^{2}$ .

10 (9 a^{2}) - 250

$10 (9 a^{2}) - 250$

Step 1.2

Factor

10

$10$ out of

- 250

$- 250$ .

10 (9 a^{2}) + 10 (- 25)

$10 (9 a^{2}) + 10 (- 25)$

Step 1.3

Factor

10

$10$ out of

10 (9 a^{2}) + 10 (- 25)

$10 (9 a^{2}) + 10 (- 25)$ .

10 (9 a^{2} - 25)

$10 (9 a^{2} - 25)$

10 (9 a^{2} - 25)

$10 (9 a^{2} - 25)$

Step 2

Rewrite

9 a^{2}

$9 a^{2}$ as

{(3 a)}^{2}

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

10 ({(3 a)}^{2} - 25)

$10 ({(3 a)}^{2} - 25)$

Step 3

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

10 ({(3 a)}^{2} - 5^{2})

$10 ({(3 a)}^{2} - 5^{2})$

Step 4

Factor.

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Step 4.1

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 a

$a = 3 a$ and

b = 5

$b = 5$ .

10 ((3 a + 5) (3 a - 5))

$10 ((3 a + 5) (3 a - 5))$

Step 4.2

Remove unnecessary parentheses.

10 (3 a + 5) (3 a - 5)

$10 (3 a + 5) (3 a - 5)$

10 (3 a + 5) (3 a - 5)

$10 (3 a + 5) (3 a - 5)$