Pre-Algebra Examples

${(3 a - b)}^{2} - {(2 a + 5 b)}^{2}$

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 a - b$ and $b = 2 a + 5 b$ .

$(3 a - b + 2 a + 5 b) (3 a - b - (2 a + 5 b))$

Step 2

Simplify.

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Step 2.1

Add $3 a$ and $2 a$ .

$(5 a - b + 5 b) (3 a - b - (2 a + 5 b))$

Step 2.2

Add $- b$ and $5 b$ .

$(5 a + 4 b) (3 a - b - (2 a + 5 b))$

Step 2.3

Apply the distributive property.

$(5 a + 4 b) (3 a - b - (2 a) - (5 b))$

Step 2.4

Multiply $2$ by $- 1$ .

$(5 a + 4 b) (3 a - b - 2 a - (5 b))$

Step 2.5

Multiply $5$ by $- 1$ .

$(5 a + 4 b) (3 a - b - 2 a - 5 b)$

Step 2.6

Subtract $2 a$ from $3 a$ .

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

Step 2.7

Subtract $5 b$ from $- b$ .

$(5 a + 4 b) (a - 6 b)$