Calculus Examples

$(8 a^{2} - 6 a b + 4 b^{2}) - (3 a^{2} + 5 a b - 4 b^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$8 a^{2} - 6 a b + 4 b^{2} - (3 a^{2}) - (5 a b) - (- 4 b^{2})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $3$ by $- 1$ .

$8 a^{2} - 6 a b + 4 b^{2} - 3 a^{2} - (5 a b) - (- 4 b^{2})$

Step 1.2.2

Multiply $5$ by $- 1$ .

$8 a^{2} - 6 a b + 4 b^{2} - 3 a^{2} - 5 (a b) - (- 4 b^{2})$

Step 1.2.3

Multiply $- 4$ by $- 1$ .

$8 a^{2} - 6 a b + 4 b^{2} - 3 a^{2} - 5 (a b) + 4 b^{2}$

$8 a^{2} - 6 a b + 4 b^{2} - 3 a^{2} - 5 a b + 4 b^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $3 a^{2}$ from $8 a^{2}$ .

$5 a^{2} - 6 a b + 4 b^{2} - 5 a b + 4 b^{2}$

Step 2.2

Subtract $5 a b$ from $- 6 a b$ .

$5 a^{2} + 4 b^{2} - 11 a b + 4 b^{2}$

Step 2.3

Add $4 b^{2}$ and $4 b^{2}$ .

$5 a^{2} + 8 b^{2} - 11 a b$