Factor
\left(2a-b-c\right)\left(a+2b+3c\right)
Evaluate
\left(2a-b-c\right)\left(a+2b+3c\right)
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2a^{2}+\left(3b+5c\right)a-2b^{2}-3c^{2}-5bc
Consider 2a^{2}-2b^{2}-3c^{2}+3ab+5ac-5bc as a polynomial over variable a.
\left(2a-b-c\right)\left(a+2b+3c\right)
Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power 2a^{2} and n divides the constant factor -2b^{2}-5bc-3c^{2}. One such factor is 2a-b-c. Factor the polynomial by dividing it by this factor.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
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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}