Basic Math Examples

$16 {(3 k - y)}^{2} - 81 y^{2}$

Step 1

Rewrite $16 {(3 k - y)}^{2}$ as ${(4 (3 k - y))}^{2}$ .

${(4 (3 k - y))}^{2} - 81 y^{2}$

Step 2

Rewrite $81 y^{2}$ as ${(9 y)}^{2}$ .

${(4 (3 k - y))}^{2} - {(9 y)}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 (3 k - y)$ and $b = 9 y$ .

$(4 (3 k - y) + 9 y) (4 (3 k - y) - (9 y))$

Step 4

Simplify.

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Step 4.1

Apply the distributive property.

$(4 (3 k) + 4 (- y) + 9 y) (4 (3 k - y) - (9 y))$

Step 4.2

Multiply $3$ by $4$ .

$(12 k + 4 (- y) + 9 y) (4 (3 k - y) - (9 y))$

Step 4.3

Multiply $- 1$ by $4$ .

$(12 k - 4 y + 9 y) (4 (3 k - y) - (9 y))$

Step 4.4

Add $- 4 y$ and $9 y$ .

$(12 k + 5 y) (4 (3 k - y) - (9 y))$

Step 4.5

Apply the distributive property.

$(12 k + 5 y) (4 (3 k) + 4 (- y) - (9 y))$

Step 4.6

Multiply $3$ by $4$ .

$(12 k + 5 y) (12 k + 4 (- y) - (9 y))$

Step 4.7

Multiply $- 1$ by $4$ .

$(12 k + 5 y) (12 k - 4 y - (9 y))$

Step 4.8

Multiply $9$ by $- 1$ .

$(12 k + 5 y) (12 k - 4 y - 9 y)$

Step 4.9

Subtract $9 y$ from $- 4 y$ .

$(12 k + 5 y) (12 k - 13 y)$