Solve 4x^4+18x^3+27x^2+27/2x

$$4 { x }^{ 4 } +18 { x }^{ 3 } +27 { x }^{ 2 } + \frac{ 27 }{ 2 } x$$

Factor

$$\frac{x\left(2x+3\right)^{3}}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{8x^{4}+36x^{3}+54x^{2}+27x}{2}$$

Consider 8x^{4}+36x^{3}+54x^{2}+27x. Factor out x.

$$x\left(8x^{3}+36x^{2}+54x+27\right)$$

Consider 8x^{3}+36x^{2}+54x+27. Use the binomial cube formula, a^{3}+3a^{2}b+3ab^{2}+b^{3}=\left(a+b\right)^{3}, where a=2x and b=3.

$$\left(2x+3\right)^{3}$$

Rewrite the complete factored expression.

$$\frac{x\left(2x+3\right)^{3}}{2}$$

Evaluate

$$\frac{x\left(2x+3\right)^{3}}{2}$$