Algebra Examples

$25 a^{2} - 16 {(a - b)}^{2}$

Step 1

Rewrite $25 a^{2}$ as ${(5 a)}^{2}$ .

${(5 a)}^{2} - 16 {(a - b)}^{2}$

Step 2

Rewrite $16 {(a - b)}^{2}$ as ${(4 (a - b))}^{2}$ .

${(5 a)}^{2} - {(4 (a - b))}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5 a$ and $b = 4 (a - b)$ .

$(5 a + 4 (a - b)) (5 a - (4 (a - b)))$

Step 4

Simplify.

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Step 4.1

Apply the distributive property.

$(5 a + 4 a + 4 (- b)) (5 a - (4 (a - b)))$

Step 4.2

Multiply $- 1$ by $4$ .

$(5 a + 4 a - 4 b) (5 a - (4 (a - b)))$

Step 4.3

Add $5 a$ and $4 a$ .

$(9 a - 4 b) (5 a - (4 (a - b)))$

Step 4.4

Apply the distributive property.

$(9 a - 4 b) (5 a - (4 a + 4 (- b)))$

Step 4.5

Multiply $- 1$ by $4$ .

$(9 a - 4 b) (5 a - (4 a - 4 b))$

Step 4.6

Apply the distributive property.

$(9 a - 4 b) (5 a - (4 a) - (- 4 b))$

Step 4.7

Multiply $4$ by $- 1$ .

$(9 a - 4 b) (5 a - 4 a - (- 4 b))$

Step 4.8

Multiply $- 4$ by $- 1$ .

$(9 a - 4 b) (5 a - 4 a + 4 b)$

Step 4.9

Subtract $4 a$ from $5 a$ .

$(9 a - 4 b) (a + 4 b)$