Algebra Examples

$49 {(y - 4)}^{2} - 9 {(y + 2)}^{2}$

Step 1

Rewrite $49 {(y - 4)}^{2}$ as ${(7 (y - 4))}^{2}$ .

${(7 (y - 4))}^{2} - 9 {(y + 2)}^{2}$

Step 2

Rewrite $9 {(y + 2)}^{2}$ as ${(3 (y + 2))}^{2}$ .

${(7 (y - 4))}^{2} - {(3 (y + 2))}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 7 (y - 4)$ and $b = 3 (y + 2)$ .

$(7 (y - 4) + 3 (y + 2)) (7 (y - 4) - (3 (y + 2)))$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Apply the distributive property.

$(7 y + 7 \cdot - 4 + 3 (y + 2)) (7 (y - 4) - (3 (y + 2)))$

Step 4.2

Multiply $7$ by $- 4$ .

$(7 y - 28 + 3 (y + 2)) (7 (y - 4) - (3 (y + 2)))$

Step 4.3

Apply the distributive property.

$(7 y - 28 + 3 y + 3 \cdot 2) (7 (y - 4) - (3 (y + 2)))$

Step 4.4

Multiply $3$ by $2$ .

$(7 y - 28 + 3 y + 6) (7 (y - 4) - (3 (y + 2)))$

Step 4.5

Add $7 y$ and $3 y$ .

$(10 y - 28 + 6) (7 (y - 4) - (3 (y + 2)))$

Step 4.6

Add $- 28$ and $6$ .

$(10 y - 22) (7 (y - 4) - (3 (y + 2)))$

Step 4.7

Factor $2$ out of $10 y - 22$ .

Tap for more steps...

Step 4.7.1

Factor $2$ out of $10 y$ .

$(2 (5 y) - 22) (7 (y - 4) - (3 (y + 2)))$

Step 4.7.2

Factor $2$ out of $- 22$ .

$(2 (5 y) + 2 (- 11)) (7 (y - 4) - (3 (y + 2)))$

Step 4.7.3

Factor $2$ out of $2 (5 y) + 2 (- 11)$ .

$2 (5 y - 11) (7 (y - 4) - (3 (y + 2)))$

Step 4.8

Multiply $3$ by $- 1$ .

$2 (5 y - 11) (7 (y - 4) - 3 (y + 2))$

Step 5

Apply the distributive property.

$2 (5 y - 11) (7 y + 7 \cdot - 4 - 3 (y + 2))$

Step 6

Multiply $7$ by $- 4$ .

$2 (5 y - 11) (7 y - 28 - 3 (y + 2))$

Step 7

Apply the distributive property.

$2 (5 y - 11) (7 y - 28 - 3 y - 3 \cdot 2)$

Step 8

Multiply $- 3$ by $2$ .

$2 (5 y - 11) (7 y - 28 - 3 y - 6)$

Step 9

Subtract $3 y$ from $7 y$ .

$2 (5 y - 11) (4 y - 28 - 6)$

Step 10

Subtract $6$ from $- 28$ .

$2 (5 y - 11) (4 y - 34)$

Step 11

Factor.

Tap for more steps...

Step 11.1

Factor $2$ out of $4 y - 34$ .

Tap for more steps...

Step 11.1.1

Factor $2$ out of $4 y$ .

$2 (5 y - 11) (2 (2 y) - 34)$

Step 11.1.2

Factor $2$ out of $- 34$ .

$2 (5 y - 11) (2 (2 y) + 2 (- 17))$

Step 11.1.3

Factor $2$ out of $2 (2 y) + 2 (- 17)$ .

$2 (5 y - 11) (2 (2 y - 17))$

Step 11.2

Remove unnecessary parentheses.

$2 (5 y - 11) \cdot 2 (2 y - 17)$

Step 12

Multiply $2$ by $2$ .

$4 (5 y - 11) (2 y - 17)$