Algebra Examples

$8 \cdot {(- \frac{1}{2} x^{3} y)}^{2} - 3 y^{5} - x^{6} y^{2}$

Step 1

Simplify each term.

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Step 1.1

Multiply $- \frac{1}{2} (x^{3} y)$ .

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Step 1.1.1

Combine $x^{3}$ and $\frac{1}{2}$ .

$8 \cdot {(- \frac{x^{3}}{2} y)}^{2} - 3 y^{5} - x^{6} y^{2}$

Step 1.1.2

Combine $y$ and $\frac{x^{3}}{2}$ .

$8 \cdot {(- \frac{y x^{3}}{2})}^{2} - 3 y^{5} - x^{6} y^{2}$

Step 1.2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.2.1

Apply the product rule to $- \frac{y x^{3}}{2}$ .

$8 \cdot ({(- 1)}^{2} {(\frac{y x^{3}}{2})}^{2}) - 3 y^{5} - x^{6} y^{2}$

Step 1.2.2

Apply the product rule to $\frac{y x^{3}}{2}$ .

$8 \cdot ({(- 1)}^{2} \frac{{(y x^{3})}^{2}}{2^{2}}) - 3 y^{5} - x^{6} y^{2}$

Step 1.2.3

Apply the product rule to $y x^{3}$ .

$8 \cdot ({(- 1)}^{2} \frac{y^{2} {(x^{3})}^{2}}{2^{2}}) - 3 y^{5} - x^{6} y^{2}$

Step 1.3

Raise $- 1$ to the power of $2$ .

$8 \cdot (1 \frac{y^{2} {(x^{3})}^{2}}{2^{2}}) - 3 y^{5} - x^{6} y^{2}$

Step 1.4

Multiply $\frac{y^{2} {(x^{3})}^{2}}{2^{2}}$ by $1$ .

$8 \cdot \frac{y^{2} {(x^{3})}^{2}}{2^{2}} - 3 y^{5} - x^{6} y^{2}$

Step 1.5

Multiply the exponents in ${(x^{3})}^{2}$ .

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Step 1.5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$8 \cdot \frac{y^{2} x^{3 \cdot 2}}{2^{2}} - 3 y^{5} - x^{6} y^{2}$

Step 1.5.2

Multiply $3$ by $2$ .

$8 \cdot \frac{y^{2} x^{6}}{2^{2}} - 3 y^{5} - x^{6} y^{2}$

Step 1.6

Raise $2$ to the power of $2$ .

$8 \cdot \frac{y^{2} x^{6}}{4} - 3 y^{5} - x^{6} y^{2}$

Step 1.7

Cancel the common factor of $4$ .

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Step 1.7.1

Factor $4$ out of $8$ .

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

Step 1.7.2

Cancel the common factor.

$4 \cdot 2 \cdot \frac{y^{2} x^{6}}{4} - 3 y^{5} - x^{6} y^{2}$

Step 1.7.3

Rewrite the expression.

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

$2 y^{2} x^{6} - 3 y^{5} - x^{6} y^{2}$

Step 2

Subtract $x^{6} y^{2}$ from $2 y^{2} x^{6}$ .

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Step 2.1

Move $y^{2}$ .

$- 3 y^{5} + 2 x^{6} y^{2} - x^{6} y^{2}$

Step 2.2

Subtract $x^{6} y^{2}$ from $2 x^{6} y^{2}$ .

$- 3 y^{5} + 1 x^{6} y^{2}$

Step 3

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

$- 3 y^{5} + x^{6} y^{2}$