Algebra Examples

$\frac{8 x^{3} \cdot 12 x y^{7}}{3 x^{2} y^{4}} - 15 x^{2} y^{3}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Move $x$ .

$\frac{8 (x \cdot x^{3}) \cdot (12 y^{7})}{3 x^{2} y^{4}} - 15 x^{2} y^{3}$

Step 1.1.2

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

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Step 1.1.2.1

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

$\frac{8 (x^{1} x^{3}) \cdot (12 y^{7})}{3 x^{2} y^{4}} - 15 x^{2} y^{3}$

Step 1.1.2.2

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

$\frac{8 x^{1 + 3} \cdot (12 y^{7})}{3 x^{2} y^{4}} - 15 x^{2} y^{3}$

Step 1.1.3

Add $1$ and $3$ .

$\frac{8 x^{4} \cdot (12 y^{7})}{3 x^{2} y^{4}} - 15 x^{2} y^{3}$

Step 1.2

Cancel the common factor of $x^{4}$ and $x^{2}$ .

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Step 1.2.1

Factor $x^{2}$ out of $8 x^{4} \cdot (12 y^{7})$ .

$\frac{x^{2} (8 x^{2} \cdot (12 y^{7}))}{3 x^{2} y^{4}} - 15 x^{2} y^{3}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $x^{2}$ out of $3 x^{2} y^{4}$ .

$\frac{x^{2} (8 x^{2} \cdot (12 y^{7}))}{x^{2} (3 y^{4})} - 15 x^{2} y^{3}$

Step 1.2.2.2

Cancel the common factor.

$\frac{x^{2} (8 x^{2} \cdot (12 y^{7}))}{x^{2} (3 y^{4})} - 15 x^{2} y^{3}$

Step 1.2.2.3

Rewrite the expression.

$\frac{8 x^{2} \cdot (12 y^{7})}{3 y^{4}} - 15 x^{2} y^{3}$

Step 1.3

Cancel the common factor of $12$ and $3$ .

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Step 1.3.1

Factor $3$ out of $8 x^{2} \cdot (12 y^{7})$ .

$\frac{3 (8 x^{2} \cdot (4 y^{7}))}{3 y^{4}} - 15 x^{2} y^{3}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $3$ out of $3 y^{4}$ .

$\frac{3 (8 x^{2} \cdot (4 y^{7}))}{3 (y^{4})} - 15 x^{2} y^{3}$

Step 1.3.2.2

Cancel the common factor.

$\frac{3 (8 x^{2} \cdot (4 y^{7}))}{3 y^{4}} - 15 x^{2} y^{3}$

Step 1.3.2.3

Rewrite the expression.

$\frac{8 x^{2} \cdot (4 y^{7})}{y^{4}} - 15 x^{2} y^{3}$

Step 1.4

Cancel the common factor of $y^{7}$ and $y^{4}$ .

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Step 1.4.1

Factor $y^{4}$ out of $8 x^{2} \cdot (4 y^{7})$ .

$\frac{y^{4} (8 x^{2} \cdot (4 y^{3}))}{y^{4}} - 15 x^{2} y^{3}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Multiply by $1$ .

$\frac{y^{4} (8 x^{2} \cdot (4 y^{3}))}{y^{4} \cdot 1} - 15 x^{2} y^{3}$

Step 1.4.2.2

Cancel the common factor.

$\frac{y^{4} (8 x^{2} \cdot (4 y^{3}))}{y^{4} \cdot 1} - 15 x^{2} y^{3}$

Step 1.4.2.3

Rewrite the expression.

$\frac{8 x^{2} \cdot (4 y^{3})}{1} - 15 x^{2} y^{3}$

Step 1.4.2.4

Divide $8 x^{2} \cdot (4 y^{3})$ by $1$ .

$8 x^{2} \cdot (4 y^{3}) - 15 x^{2} y^{3}$

Step 1.5

Rewrite using the commutative property of multiplication.

$8 \cdot 4 x^{2} y^{3} - 15 x^{2} y^{3}$

Step 1.6

Multiply $8$ by $4$ .

$32 x^{2} y^{3} - 15 x^{2} y^{3}$

Step 2

Subtract $15 x^{2} y^{3}$ from $32 x^{2} y^{3}$ .

$17 x^{2} y^{3}$