Basic Math Examples

$(- f) (- f^{2} + 3 f)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$- f (- f^{2}) - f (3 f)$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$- 1 \cdot - 1 f \cdot f^{2} - f (3 f)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$- 1 \cdot - 1 f \cdot f^{2} - 1 \cdot 3 f \cdot f$

Step 2

Simplify each term.

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Step 2.1

Multiply $f$ by $f^{2}$ by adding the exponents.

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Step 2.1.1

Move $f^{2}$ .

$- 1 \cdot - 1 (f^{2} f) - 1 \cdot 3 f \cdot f$

Step 2.1.2

Multiply $f^{2}$ by $f$ .

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Step 2.1.2.1

Raise $f$ to the power of $1$ .

$- 1 \cdot - 1 (f^{2} f^{1}) - 1 \cdot 3 f \cdot f$

Step 2.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 1 \cdot - 1 f^{2 + 1} - 1 \cdot 3 f \cdot f$

Step 2.1.3

Add $2$ and $1$ .

$- 1 \cdot - 1 f^{3} - 1 \cdot 3 f \cdot f$

Step 2.2

Multiply $- 1$ by $- 1$ .

$1 f^{3} - 1 \cdot 3 f \cdot f$

Step 2.3

Multiply $f^{3}$ by $1$ .

$f^{3} - 1 \cdot 3 f \cdot f$

Step 2.4

Multiply $f$ by $f$ by adding the exponents.

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Step 2.4.1

Move $f$ .

$f^{3} - 1 \cdot 3 (f \cdot f)$

Step 2.4.2

Multiply $f$ by $f$ .

$f^{3} - 1 \cdot 3 f^{2}$

Step 2.5

Multiply $- 1$ by $3$ .

$f^{3} - 3 f^{2}$