Finite Math Examples

$(4 a^{2} + 11 a f - 2 f^{2}) - (6 a^{2} - 9 a f + 18 f^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$4 a^{2} + 11 a f - 2 f^{2} - (6 a^{2}) - (- 9 a f) - (18 f^{2})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $6$ by $- 1$ .

$4 a^{2} + 11 a f - 2 f^{2} - 6 a^{2} - (- 9 a f) - (18 f^{2})$

Step 1.2.2

Multiply $- 9$ by $- 1$ .

$4 a^{2} + 11 a f - 2 f^{2} - 6 a^{2} + 9 (a f) - (18 f^{2})$

Step 1.2.3

Multiply $18$ by $- 1$ .

$4 a^{2} + 11 a f - 2 f^{2} - 6 a^{2} + 9 (a f) - 18 f^{2}$

$4 a^{2} + 11 a f - 2 f^{2} - 6 a^{2} + 9 a f - 18 f^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $6 a^{2}$ from $4 a^{2}$ .

$- 2 a^{2} + 11 a f - 2 f^{2} + 9 a f - 18 f^{2}$

Step 2.2

Add $11 a f$ and $9 a f$ .

$- 2 a^{2} - 2 f^{2} + 20 a f - 18 f^{2}$

Step 2.3

Subtract $18 f^{2}$ from $- 2 f^{2}$ .

$- 2 a^{2} - 20 f^{2} + 20 a f$