Algebra Examples

$(2 x^{5} y^{2}) (4 x y^{3}) + (x^{4} y^{4}) (3 x^{2} y)$

Step 1

Simplify each term.

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Step 1.1

Multiply $x^{5}$ by $x$ by adding the exponents.

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Step 1.1.1

Move $x$ .

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

Step 1.1.2

Multiply $x$ by $x^{5}$ .

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Step 1.1.2.1

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

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

Step 1.1.2.2

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

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

Step 1.1.3

Add $1$ and $5$ .

$2 x^{6} y^{2} (4 y^{3}) + (x^{4} y^{4}) (3 x^{2} y)$

Step 1.2

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

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Step 1.2.1

Move $y^{3}$ .

$2 x^{6} (y^{3} y^{2}) \cdot 4 + (x^{4} y^{4}) (3 x^{2} y)$

Step 1.2.2

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

$2 x^{6} y^{3 + 2} \cdot 4 + (x^{4} y^{4}) (3 x^{2} y)$

Step 1.2.3

Add $3$ and $2$ .

$2 x^{6} y^{5} \cdot 4 + (x^{4} y^{4}) (3 x^{2} y)$

Step 1.3

Multiply $4$ by $2$ .

$8 x^{6} y^{5} + (x^{4} y^{4}) (3 x^{2} y)$

Step 1.4

Rewrite using the commutative property of multiplication.

$8 x^{6} y^{5} + 3 x^{4} y^{4} (x^{2} y)$

Step 1.5

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

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Step 1.5.1

Move $x^{2}$ .

$8 x^{6} y^{5} + 3 (x^{2} x^{4}) y^{4} y$

Step 1.5.2

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

$8 x^{6} y^{5} + 3 x^{2 + 4} y^{4} y$

Step 1.5.3

Add $2$ and $4$ .

$8 x^{6} y^{5} + 3 x^{6} y^{4} y$

Step 1.6

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

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Step 1.6.1

Move $y$ .

$8 x^{6} y^{5} + 3 x^{6} (y \cdot y^{4})$

Step 1.6.2

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

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Step 1.6.2.1

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

$8 x^{6} y^{5} + 3 x^{6} (y^{1} y^{4})$

Step 1.6.2.2

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

$8 x^{6} y^{5} + 3 x^{6} y^{1 + 4}$

Step 1.6.3

Add $1$ and $4$ .

$8 x^{6} y^{5} + 3 x^{6} y^{5}$

Step 2

Add $8 x^{6} y^{5}$ and $3 x^{6} y^{5}$ .

$11 x^{6} y^{5}$