Algebra Examples

$6 x \sqrt{x^{3} y^{4}} - 7 x^{2} \sqrt{x y^{4}} + 9 x^{2} y^{2} \sqrt{x}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $x^{3} y^{4}$ as ${(x y^{2})}^{2} x$ .

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Step 1.1.1

Factor out $x^{2}$ .

$6 x \sqrt{x^{2} x y^{4}} - 7 x^{2} \sqrt{x y^{4}} + 9 x^{2} y^{2} \sqrt{x}$

Step 1.1.2

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$6 x \sqrt{x^{2} x {(y^{2})}^{2}} - 7 x^{2} \sqrt{x y^{4}} + 9 x^{2} y^{2} \sqrt{x}$

Step 1.1.3

Move $x$ .

$6 x \sqrt{x^{2} {(y^{2})}^{2} x} - 7 x^{2} \sqrt{x y^{4}} + 9 x^{2} y^{2} \sqrt{x}$

Step 1.1.4

Rewrite $x^{2} {(y^{2})}^{2}$ as ${(x y^{2})}^{2}$ .

$6 x \sqrt{{(x y^{2})}^{2} x} - 7 x^{2} \sqrt{x y^{4}} + 9 x^{2} y^{2} \sqrt{x}$

Step 1.2

Pull terms out from under the radical.

$6 x (x y^{2} \sqrt{x}) - 7 x^{2} \sqrt{x y^{4}} + 9 x^{2} y^{2} \sqrt{x}$

Step 1.3

Multiply $x$ by $x$ by adding the exponents.

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Step 1.3.1

Move $x$ .

$6 (x \cdot x) (y^{2} \sqrt{x}) - 7 x^{2} \sqrt{x y^{4}} + 9 x^{2} y^{2} \sqrt{x}$

Step 1.3.2

Multiply $x$ by $x$ .

$6 x^{2} (y^{2} \sqrt{x}) - 7 x^{2} \sqrt{x y^{4}} + 9 x^{2} y^{2} \sqrt{x}$

Step 1.4

Rewrite $x y^{4}$ as ${(y^{2})}^{2} x$ .

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Step 1.4.1

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$6 x^{2} (y^{2} \sqrt{x}) - 7 x^{2} \sqrt{x {(y^{2})}^{2}} + 9 x^{2} y^{2} \sqrt{x}$

Step 1.4.2

Reorder $x$ and ${(y^{2})}^{2}$ .

$6 x^{2} (y^{2} \sqrt{x}) - 7 x^{2} \sqrt{{(y^{2})}^{2} x} + 9 x^{2} y^{2} \sqrt{x}$

Step 1.5

Pull terms out from under the radical.

$6 x^{2} (y^{2} \sqrt{x}) - 7 x^{2} (y^{2} \sqrt{x}) + 9 x^{2} y^{2} \sqrt{x}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $7 x^{2} (y^{2} \sqrt{x})$ from $6 x^{2} (y^{2} \sqrt{x})$ .

$- x^{2} y^{2} \sqrt{x} + 9 x^{2} y^{2} \sqrt{x}$

Step 2.2

Add $- x^{2} y^{2} \sqrt{x}$ and $9 x^{2} y^{2} \sqrt{x}$ .

$8 x^{2} y^{2} \sqrt{x}$