Factor
\frac{\left(2x-12y+3\right)\left(2x+12y-3\right)}{36}
Evaluate
-\frac{\left(12y-3\right)^{2}}{36}+\frac{x^{2}}{9}
Quiz
Algebra
5 problems similar to:
\frac { 1 } { 9 } x ^ { 2 } - 4 y ^ { 2 } + 2 y - \frac { 1 } { 4 }
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\frac{4x^{2}-144y^{2}+72y-9}{36}
Factor out \frac{1}{36}.
4x^{2}-\left(144y^{2}-72y+9\right)
Consider 4x^{2}-144y^{2}+72y-9. Rewrite as difference of two terms.
\left(2x\right)^{2}-\left(3-12y\right)^{2}
Rewrite the terms as squares.
\left(2x-3+12y\right)\left(2x+3-12y\right)
The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(2x+12y-3\right)\left(2x-12y+3\right)
Reorder the terms.
\frac{\left(2x+12y-3\right)\left(2x-12y+3\right)}{36}
Rewrite the complete factored expression.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}