Algebra Examples

$w^{3} (3 w^{2} + 2 w) + 5 w^{4}$

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.

$w^{3} (3 w^{2}) + w^{3} (2 w) + 5 w^{4}$

Step 2.2

Rewrite using the commutative property of multiplication.

$3 w^{3} w^{2} + w^{3} (2 w) + 5 w^{4}$

Step 2.3

Rewrite using the commutative property of multiplication.

$3 w^{3} w^{2} + 2 w^{3} w + 5 w^{4}$

Step 2.4

Simplify each term.

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Step 2.4.1

Multiply $w^{3}$ by $w^{2}$ by adding the exponents.

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Step 2.4.1.1

Move $w^{2}$ .

$3 (w^{2} w^{3}) + 2 w^{3} w + 5 w^{4}$

Step 2.4.1.2

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

$3 w^{2 + 3} + 2 w^{3} w + 5 w^{4}$

Step 2.4.1.3

Add $2$ and $3$ .

$3 w^{5} + 2 w^{3} w + 5 w^{4}$

Step 2.4.2

Multiply $w^{3}$ by $w$ by adding the exponents.

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Step 2.4.2.1

Move $w$ .

$3 w^{5} + 2 (w \cdot w^{3}) + 5 w^{4}$

Step 2.4.2.2

Multiply $w$ by $w^{3}$ .

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Step 2.4.2.2.1

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

$3 w^{5} + 2 (w^{1} w^{3}) + 5 w^{4}$

Step 2.4.2.2.2

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

$3 w^{5} + 2 w^{1 + 3} + 5 w^{4}$

Step 2.4.2.3

Add $1$ and $3$ .

$3 w^{5} + 2 w^{4} + 5 w^{4}$

Step 3

Add $2 w^{4}$ and $5 w^{4}$ .

$3 w^{5} + 7 w^{4}$