Algebra Examples

$4 x^{7} y^{6} + 9 x^{3} y \cdot 2 x^{4} y^{5}$

Step 1

Simplify each term.

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Step 1.1

Multiply $x^{3}$ by $x^{4}$ by adding the exponents.

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Step 1.1.1

Move $x^{4}$ .

$4 x^{7} y^{6} + 9 (x^{4} x^{3}) y \cdot (2 y^{5})$

Step 1.1.2

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

$4 x^{7} y^{6} + 9 x^{4 + 3} y \cdot (2 y^{5})$

Step 1.1.3

Add $4$ and $3$ .

$4 x^{7} y^{6} + 9 x^{7} y \cdot (2 y^{5})$

Step 1.2

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

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Step 1.2.1

Move $y^{5}$ .

$4 x^{7} y^{6} + 9 x^{7} (y^{5} y) \cdot 2$

Step 1.2.2

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

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Step 1.2.2.1

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

$4 x^{7} y^{6} + 9 x^{7} (y^{5} y^{1}) \cdot 2$

Step 1.2.2.2

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

$4 x^{7} y^{6} + 9 x^{7} y^{5 + 1} \cdot 2$

Step 1.2.3

Add $5$ and $1$ .

$4 x^{7} y^{6} + 9 x^{7} y^{6} \cdot 2$

Step 1.3

Multiply $2$ by $9$ .

$4 x^{7} y^{6} + 18 x^{7} y^{6}$

Step 2

Add $4 x^{7} y^{6}$ and $18 x^{7} y^{6}$ .

$22 x^{7} y^{6}$