Final Answer
$y=-\frac{1}{2}+\sqrt{x^3\left(x+4\right)^3+\frac{1}{4}},\:y=-\frac{1}{2}-\sqrt{x^3\left(x+4\right)^3+\frac{1}{4}}$
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Step-by-step Solution
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1
Factor the polynomial $\left(x^2+4x\right)$ by it's greatest common factor (GCF): $x$
$\left(x\left(x+4\right)\right)^3=y+y^2$
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$\left(x\left(x+4\right)\right)^3=y+y^2$
Learn how to solve problems step by step online. Solve the equation (x^2+4x)^3=y+y^2. Factor the polynomial \left(x^2+4x\right) by it's greatest common factor (GCF): x. The power of a product is equal to the product of it's factors raised to the same power. Rearrange the equation. Factor the polynomial y+y^2. Add and subtract \left(\frac{b}{2}\right)^2, where in this case b equals 1.
Final Answer
$y=-\frac{1}{2}+\sqrt{x^3\left(x+4\right)^3+\frac{1}{4}},\:y=-\frac{1}{2}-\sqrt{x^3\left(x+4\right)^3+\frac{1}{4}}$