Basic Math Examples

$64 - {(r + 2 t)}^{2}$

Step 1

Rewrite $64$ as $8^{2}$ .

$8^{2} - {(r + 2 t)}^{2}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 8$ and $b = r + 2 t$ .

$(8 + r + 2 t) (8 - (r + 2 t))$

Step 3

Simplify.

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Step 3.1

Apply the distributive property.

$(8 + r + 2 t) (8 - r - (2 t))$

Step 3.2

Multiply $2$ by $- 1$ .

$(8 + r + 2 t) (8 - r - 2 t)$

Step 4

Factor.

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Step 4.1

Factor $- 1$ out of $8 - r - 2 t$ .

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Step 4.1.1

Move $8$ .

$(8 + r + 2 t) (- r - 2 t + 8)$

Step 4.1.2

Factor $- 1$ out of $- r$ .

$(8 + r + 2 t) (- (r) - 2 t + 8)$

Step 4.1.3

Factor $- 1$ out of $- 2 t$ .

$(8 + r + 2 t) (- (r) - (2 t) + 8)$

Step 4.1.4

Rewrite $8$ as $- 1 (- 8)$ .

$(8 + r + 2 t) (- (r) - (2 t) - 1 (- 8))$

Step 4.1.5

Factor $- 1$ out of $- (r) - (2 t)$ .

$(8 + r + 2 t) (- (r + 2 t) - 1 (- 8))$

Step 4.1.6

Factor $- 1$ out of $- (r + 2 t) - 1 (- 8)$ .

$(8 + r + 2 t) (- (r + 2 t - 8))$

Step 4.2

Remove unnecessary parentheses.

$(8 + r + 2 t) \cdot - 1 (r + 2 t - 8)$

Step 5

Factor out negative.

$- ((8 + r + 2 t) (r + 2 t - 8))$

Step 6

Remove unnecessary parentheses.

$- (8 + r + 2 t) (r + 2 t - 8)$