Algebra Examples

$(f^{3} - 5 f + 25) - (4 f^{2} - 12 f + 9)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$f^{3} - 5 f + 25 - (4 f^{2}) - (- 12 f) - 1 \cdot 9$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $4$ by $- 1$ .

$f^{3} - 5 f + 25 - 4 f^{2} - (- 12 f) - 1 \cdot 9$

Step 2.2.2

Multiply $- 12$ by $- 1$ .

$f^{3} - 5 f + 25 - 4 f^{2} + 12 f - 1 \cdot 9$

Step 2.2.3

Multiply $- 1$ by $9$ .

$f^{3} - 5 f + 25 - 4 f^{2} + 12 f - 9$

Step 3

Simplify by adding terms.

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Step 3.1

Add $- 5 f$ and $12 f$ .

$f^{3} + 7 f + 25 - 4 f^{2} - 9$

Step 3.2

Simplify the expression.

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Step 3.2.1

Subtract $9$ from $25$ .

$f^{3} + 7 f - 4 f^{2} + 16$

Step 3.2.2

Move $7 f$ .

$f^{3} - 4 f^{2} + 7 f + 16$