Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify each term.

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Step 2.1

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

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Step 2.1.1

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

$4 x + x^{2 + 4} - {(y^{2})}^{3} + {(3 x y)}^{2}$

Step 2.1.2

Add $2$ and $4$ .

$4 x + x^{6} - {(y^{2})}^{3} + {(3 x y)}^{2}$

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

Multiply $2$ by $3$ .

$4 x + x^{6} - y^{6} + {(3 x y)}^{2}$

Step 2.3

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

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Step 2.3.1

Apply the product rule to $3 x y$ .

$4 x + x^{6} - y^{6} + {(3 x)}^{2} y^{2}$

Step 2.3.2

Apply the product rule to $3 x$ .

$4 x + x^{6} - y^{6} + 3^{2} x^{2} y^{2}$

Step 2.4

Raise $3$ to the power of $2$ .

$4 x + x^{6} - y^{6} + 9 x^{2} y^{2}$

Step 3

Move $4 x$ .

$x^{6} - y^{6} + 9 x^{2} y^{2} + 4 x$