Write as a Function of x 3y+ cube root of x=(x+5)^2

$3 y + \sqrt[3]{x} = {(x + 5)}^{2}$

Step 1

Simplify ${(x + 5)}^{2}$ .

Rewrite.

$3 y + \sqrt[3]{x} = 0 + 0 + {(x + 5)}^{2}$

Rewrite ${(x + 5)}^{2}$ as $(x + 5) (x + 5)$ .

$3 y + \sqrt[3]{x} = (x + 5) (x + 5)$

Expand $(x + 5) (x + 5)$ using the FOIL Method.

Apply the distributive property.

$3 y + \sqrt[3]{x} = x (x + 5) + 5 (x + 5)$

Apply the distributive property.

$3 y + \sqrt[3]{x} = x \cdot x + x \cdot 5 + 5 (x + 5)$

Apply the distributive property.

$3 y + \sqrt[3]{x} = x \cdot x + x \cdot 5 + 5 x + 5 \cdot 5$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$3 y + \sqrt[3]{x} = x^{2} + x \cdot 5 + 5 x + 5 \cdot 5$

Move $5$ to the left of $x$ .

$3 y + \sqrt[3]{x} = x^{2} + 5 \cdot x + 5 x + 5 \cdot 5$

Multiply $5$ by $5$ .

$3 y + \sqrt[3]{x} = x^{2} + 5 x + 5 x + 25$

Add $5 x$ and $5 x$ .

$3 y + \sqrt[3]{x} = x^{2} + 10 x + 25$

Step 2

Subtract $\sqrt[3]{x}$ from both sides of the equation.

$3 y = x^{2} + 10 x + 25 - \sqrt[3]{x}$

Step 3

Divide each term in $3 y = x^{2} + 10 x + 25 - \sqrt[3]{x}$ by $3$ and simplify.

Divide each term in $3 y = x^{2} + 10 x + 25 - \sqrt[3]{x}$ by $3$ .

$\frac{3 y}{3} = \frac{x^{2}}{3} + \frac{10 x}{3} + \frac{25}{3} + \frac{- \sqrt[3]{x}}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{x^{2}}{3} + \frac{10 x}{3} + \frac{25}{3} + \frac{- \sqrt[3]{x}}{3}$

Divide $y$ by $1$ .

$y = \frac{x^{2}}{3} + \frac{10 x}{3} + \frac{25}{3} + \frac{- \sqrt[3]{x}}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{x^{2}}{3} + \frac{10 x}{3} + \frac{25}{3} - \frac{\sqrt[3]{x}}{3}$

Step 4

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = \frac{x^{2}}{3} + \frac{10 x}{3} + \frac{25}{3} - \frac{\sqrt[3]{x}}{3}$

Write as a Function of x 3y+ cube root of x=(x+5)^2

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