Algebra Examples

$(10 a^{2} b - 8 a + 5 a^{2} b - 2 a b) - (a b^{2} - 6 a b - 2 a + 3 a b)$

Step 1

Simplify each term.

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Step 1.1

Add $- 6 a b$ and $3 a b$ .

$10 a^{2} b - 8 a + 5 a^{2} b - 2 a b - (a b^{2} - 2 a - 3 a b)$

Step 1.2

Apply the distributive property.

$10 a^{2} b - 8 a + 5 a^{2} b - 2 a b - (a b^{2}) - (- 2 a) - (- 3 a b)$

Step 1.3

Simplify.

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Step 1.3.1

Multiply $- 2$ by $- 1$ .

$10 a^{2} b - 8 a + 5 a^{2} b - 2 a b - a b^{2} + 2 a - (- 3 a b)$

Step 1.3.2

Multiply $- 3$ by $- 1$ .

$10 a^{2} b - 8 a + 5 a^{2} b - 2 a b - a b^{2} + 2 a + 3 (a b)$

$10 a^{2} b - 8 a + 5 a^{2} b - 2 a b - a b^{2} + 2 a + 3 a b$

Step 2

Simplify by adding terms.

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Step 2.1

Add $10 a^{2} b$ and $5 a^{2} b$ .

$- 8 a + 15 a^{2} b - 2 a b - a b^{2} + 2 a + 3 a b$

Step 2.2

Add $- 8 a$ and $2 a$ .

$- 6 a + 15 a^{2} b - 2 a b - a b^{2} + 3 a b$

Step 2.3

Add $- 2 a b$ and $3 a b$ .

$- 6 a + 15 a^{2} b + 1 a b - a b^{2}$

Step 2.4

Multiply $a$ by $1$ .

$- 6 a + 15 a^{2} b + a b - a b^{2}$