Algebra Examples

$\frac{16 x^{9} y^{5} - 4 x^{9} y^{5}}{2 x^{3} y^{5}} + 3 x \cdot 7 x^{5}$

Step 1

Subtract $4 x^{9} y^{5}$ from $16 x^{9} y^{5}$ .

$\frac{12 x^{9} y^{5}}{2 x^{3} y^{5}} + 3 x \cdot (7 x^{5})$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $12$ and $2$ .

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Step 2.1.1

Factor $2$ out of $12 x^{9} y^{5}$ .

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

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $2 x^{3} y^{5}$ .

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

Step 2.1.2.2

Cancel the common factor.

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

Step 2.1.2.3

Rewrite the expression.

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

Step 2.2

Cancel the common factor of $x^{9}$ and $x^{3}$ .

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Step 2.2.1

Factor $x^{3}$ out of $6 x^{9} y^{5}$ .

$\frac{x^{3} (6 x^{6} y^{5})}{x^{3} y^{5}} + 3 x \cdot (7 x^{5})$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $x^{3}$ out of $x^{3} y^{5}$ .

$\frac{x^{3} (6 x^{6} y^{5})}{x^{3} (y^{5})} + 3 x \cdot (7 x^{5})$

Step 2.2.2.2

Cancel the common factor.

$\frac{x^{3} (6 x^{6} y^{5})}{x^{3} y^{5}} + 3 x \cdot (7 x^{5})$

Step 2.2.2.3

Rewrite the expression.

$\frac{6 x^{6} y^{5}}{y^{5}} + 3 x \cdot (7 x^{5})$

Step 2.3

Cancel the common factor of $y^{5}$ .

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Step 2.3.1

Cancel the common factor.

$\frac{6 x^{6} y^{5}}{y^{5}} + 3 x \cdot (7 x^{5})$

Step 2.3.2

Divide $6 x^{6}$ by $1$ .

$6 x^{6} + 3 x \cdot (7 x^{5})$

Step 2.4

Rewrite using the commutative property of multiplication.

$6 x^{6} + 3 \cdot 7 x \cdot x^{5}$

Step 2.5

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

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Step 2.5.1

Move $x^{5}$ .

$6 x^{6} + 3 \cdot 7 (x^{5} x)$

Step 2.5.2

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

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Step 2.5.2.1

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

$6 x^{6} + 3 \cdot 7 (x^{5} x^{1})$

Step 2.5.2.2

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

$6 x^{6} + 3 \cdot 7 x^{5 + 1}$

Step 2.5.3

Add $5$ and $1$ .

$6 x^{6} + 3 \cdot 7 x^{6}$

Step 2.6

Multiply $3$ by $7$ .

$6 x^{6} + 21 x^{6}$

Step 3

Add $6 x^{6}$ and $21 x^{6}$ .

$27 x^{6}$