Type a math problem or upload a photo, screenshot, handwritten question...
error msg
- Algebra
- Calculus
- Trigonometry
- Matrix
- Differential
- Integral
- Trigonometry
- Letters
Question
3a^{2}-27
Factor the expression
3\left(a-3\right)\left(a+3\right)
Evaluate
3a^{2}-27
\text{Factor out }3\text{ from the expression}
3\left(a^{2}-9\right)
Solution
More Steps
Evaluate
a^{2}-9
Rewrite the expression in exponential form
a^{2}-3^{2}
\text{Use }a^2-b^2=(a-b)(a+b)\text{ to factor the expression}
\left(a-3\right)\left(a+3\right)
3\left(a-3\right)\left(a+3\right)
Show Solutions
Find the roots
a_{1}=-3,a_{2}=3
Evaluate
3a^{2}-27
To find the roots of the expression,set the expression equal to 0
3a^{2}-27=0
Move the constant to the right-hand side and change its sign
3a^{2}=0+27
Removing 0 doesn't change the value,so remove it from the expression
3a^{2}=27
Divide both sides
\frac{3a^{2}}{3}=\frac{27}{3}
Divide the numbers
a^{2}=\frac{27}{3}
Divide the numbers
More Steps
Evaluate
\frac{27}{3}
Reduce the numbers
\frac{9}{1}
Calculate
9
a^{2}=9
Take the root of both sides of the equation and remember to use both positive and negative roots
a=\pm \sqrt{9}
Simplify the expression
More Steps
Evaluate
\sqrt{9}
\text{Write the number in exponential form with the base of }3
\sqrt{3^{2}}
\text{Reduce the index of the radical and exponent with }2
3
a=\pm 3
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&a=3\\&a=-3\end{align}
Solution
a_{1}=-3,a_{2}=3
Show Solutions
