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Question
3x-27x^{3}
Factor the expression
3x\left(1-3x\right)\left(1+3x\right)
Evaluate
3x-27x^{3}
\text{Factor out }3x\text{ from the expression}
3x\left(1-9x^{2}\right)
Solution
More Steps
Evaluate
1-9x^{2}
Rewrite the expression in exponential form
1^{2}-\left(3x\right)^{2}
\text{Use }a^2-b^2=(a-b)(a+b)\text{ to factor the expression}
\left(1-3x\right)\left(1+3x\right)
3x\left(1-3x\right)\left(1+3x\right)
Show Solutions
Find the roots
x_{1}=-\frac{1}{3},x_{2}=0,x_{3}=\frac{1}{3}
Alternative Form
x_{1}=-0.\dot{3},x_{2}=0,x_{3}=0.\dot{3}
Evaluate
3x-27x^{3}
To find the roots of the expression,set the expression equal to 0
3x-27x^{3}=0
Factor the expression
3x\left(1-9x^{2}\right)=0
Divide both sides
x\left(1-9x^{2}\right)=0
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=0\\&1-9x^{2}=0\end{align}
Solve the equation
More Steps
Evaluate
1-9x^{2}=0
Move the constant to the right-hand side and change its sign
-9x^{2}=0-1
Removing 0 doesn't change the value,so remove it from the expression
-9x^{2}=-1
Change the signs on both sides of the equation
9x^{2}=1
Divide both sides
\frac{9x^{2}}{9}=\frac{1}{9}
Divide the numbers
x^{2}=\frac{1}{9}
Take the root of both sides of the equation and remember to use both positive and negative roots
x=\pm \sqrt{\frac{1}{9}}
Simplify the expression
More Steps
Evaluate
\sqrt{\frac{1}{9}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt{1}}{\sqrt{9}}
Simplify the radical expression
\frac{1}{\sqrt{9}}
Simplify the radical expression
\frac{1}{3}
x=\pm \frac{1}{3}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=\frac{1}{3}\\&x=-\frac{1}{3}\end{align}
\begin{align}&x=0\\&x=\frac{1}{3}\\&x=-\frac{1}{3}\end{align}
Solution
x_{1}=-\frac{1}{3},x_{2}=0,x_{3}=\frac{1}{3}
Alternative Form
x_{1}=-0.\dot{3},x_{2}=0,x_{3}=0.\dot{3}
Show Solutions
