Algebra Examples

${(- 5 x^{2} y)}^{2} \cdot x y^{2} - 9 x^{5} y^{4}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Apply the product rule to $- 5 x^{2} y$ .

${(- 5 x^{2})}^{2} y^{2} \cdot (x y^{2}) - 9 x^{5} y^{4}$

Step 1.1.2

Apply the product rule to $- 5 x^{2}$ .

${(- 5)}^{2} {(x^{2})}^{2} y^{2} \cdot (x y^{2}) - 9 x^{5} y^{4}$

Step 1.2

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

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Step 1.2.1

Move $y^{2}$ .

${(- 5)}^{2} {(x^{2})}^{2} (y^{2} y^{2}) \cdot x - 9 x^{5} y^{4}$

Step 1.2.2

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

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

Step 1.2.3

Add $2$ and $2$ .

${(- 5)}^{2} {(x^{2})}^{2} y^{4} \cdot x - 9 x^{5} y^{4}$

Step 1.3

Raise $- 5$ to the power of $2$ .

$25 {(x^{2})}^{2} y^{4} \cdot x - 9 x^{5} y^{4}$

Step 1.4

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

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Step 1.4.1

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

$25 x^{2 \cdot 2} y^{4} \cdot x - 9 x^{5} y^{4}$

Step 1.4.2

Multiply $2$ by $2$ .

$25 x^{4} y^{4} \cdot x - 9 x^{5} y^{4}$

Step 1.5

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

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Step 1.5.1

Move $x$ .

$25 (x \cdot x^{4}) y^{4} - 9 x^{5} y^{4}$

Step 1.5.2

Multiply $x$ by $x^{4}$ .

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Step 1.5.2.1

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

$25 (x^{1} x^{4}) y^{4} - 9 x^{5} y^{4}$

Step 1.5.2.2

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

$25 x^{1 + 4} y^{4} - 9 x^{5} y^{4}$

Step 1.5.3

Add $1$ and $4$ .

$25 x^{5} y^{4} - 9 x^{5} y^{4}$

Step 2

Subtract $9 x^{5} y^{4}$ from $25 x^{5} y^{4}$ .

$16 x^{5} y^{4}$