Algebra Examples

$- 5 g^{2} (g^{2} - 4 g)$

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

Apply the distributive property.

$- 5 g^{2} g^{2} - 5 g^{2} (- 4 g)$

Step 3

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

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Step 3.1

Move $g^{2}$ .

$- 5 (g^{2} g^{2}) - 5 g^{2} (- 4 g)$

Step 3.2

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

$- 5 g^{2 + 2} - 5 g^{2} (- 4 g)$

Step 3.3

Add $2$ and $2$ .

$- 5 g^{4} - 5 g^{2} (- 4 g)$

Step 4

Rewrite using the commutative property of multiplication.

$- 5 g^{4} - 5 \cdot - 4 g^{2} g$

Step 5

Simplify each term.

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Step 5.1

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

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Step 5.1.1

Move $g$ .

$- 5 g^{4} - 5 \cdot - 4 (g \cdot g^{2})$

Step 5.1.2

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

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Step 5.1.2.1

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

$- 5 g^{4} - 5 \cdot - 4 (g^{1} g^{2})$

Step 5.1.2.2

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

$- 5 g^{4} - 5 \cdot - 4 g^{1 + 2}$

Step 5.1.3

Add $1$ and $2$ .

$- 5 g^{4} - 5 \cdot - 4 g^{3}$

Step 5.2

Multiply $- 5$ by $- 4$ .

$- 5 g^{4} + 20 g^{3}$