Algebra Examples

$(- 2 y^{4}) \cdot {(x y^{3})}^{2} - 13 x^{2} y^{10}$

Step 1

Simplify each term.

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Step 1.1

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

$- 2 y^{4} \cdot (x^{2} {(y^{3})}^{2}) - 13 x^{2} y^{10}$

Step 1.2

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

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Step 1.2.1

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

$- 2 y^{4} \cdot (x^{2} y^{3 \cdot 2}) - 13 x^{2} y^{10}$

Step 1.2.2

Multiply $3$ by $2$ .

$- 2 y^{4} \cdot (x^{2} y^{6}) - 13 x^{2} y^{10}$

Step 1.3

Multiply $y^{4}$ by $y^{6}$ by adding the exponents.

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Step 1.3.1

Move $y^{6}$ .

$- 2 (y^{6} y^{4}) \cdot x^{2} - 13 x^{2} y^{10}$

Step 1.3.2

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

$- 2 y^{6 + 4} \cdot x^{2} - 13 x^{2} y^{10}$

Step 1.3.3

Add $6$ and $4$ .

$- 2 y^{10} \cdot x^{2} - 13 x^{2} y^{10}$

$- 2 y^{10} x^{2} - 13 x^{2} y^{10}$

Step 2

Subtract $13 x^{2} y^{10}$ from $- 2 y^{10} x^{2}$ .

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Step 2.1

Move $y^{10}$ .

$- 2 x^{2} y^{10} - 13 x^{2} y^{10}$

Step 2.2

Subtract $13 x^{2} y^{10}$ from $- 2 x^{2} y^{10}$ .

$- 15 x^{2} y^{10}$