Algebra Examples

$a y \cdot (a^{3} + 4 y^{4})$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Apply the distributive property.

$a y a^{3} + a y (4 y^{4})$

Step 1.2

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

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Step 1.2.1

Move $a^{3}$ .

$a^{3} a y + a y (4 y^{4})$

Step 1.2.2

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

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Step 1.2.2.1

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

$a^{3} a^{1} y + a y (4 y^{4})$

Step 1.2.2.2

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

$a^{3 + 1} y + a y (4 y^{4})$

Step 1.2.3

Add $3$ and $1$ .

$a^{4} y + a y (4 y^{4})$

Step 1.3

Rewrite using the commutative property of multiplication.

$a^{4} y + 4 a y \cdot y^{4}$

Step 1.4

Multiply $y$ by $y^{4}$ by adding the exponents.

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Step 1.4.1

Move $y^{4}$ .

$a^{4} y + 4 a (y^{4} y)$

Step 1.4.2

Multiply $y^{4}$ by $y$ .

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Step 1.4.2.1

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

$a^{4} y + 4 a (y^{4} y^{1})$

Step 1.4.2.2

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

$a^{4} y + 4 a y^{4 + 1}$

Step 1.4.3

Add $4$ and $1$ .

$a^{4} y + 4 a y^{5}$

Step 2

The largest exponent is the degree of the polynomial.

$6$