Evaluate
7+5x-6x^{2}
Expand
7+5x-6x^{2}
Graph
Share
Copied to clipboard
x-2x^{2}-2+4x-\left(2x-3\right)\left(2x+3\right)
Apply the distributive property by multiplying each term of x-2 by each term of 1-2x.
5x-2x^{2}-2-\left(2x-3\right)\left(2x+3\right)
Combine x and 4x to get 5x.
5x-2x^{2}-2-\left(\left(2x\right)^{2}-3^{2}\right)
Consider \left(2x-3\right)\left(2x+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
5x-2x^{2}-2-\left(2^{2}x^{2}-3^{2}\right)
Expand \left(2x\right)^{2}.
5x-2x^{2}-2-\left(4x^{2}-3^{2}\right)
Calculate 2 to the power of 2 and get 4.
5x-2x^{2}-2-\left(4x^{2}-9\right)
Calculate 3 to the power of 2 and get 9.
5x-2x^{2}-2-4x^{2}-\left(-9\right)
To find the opposite of 4x^{2}-9, find the opposite of each term.
5x-2x^{2}-2-4x^{2}+9
The opposite of -9 is 9.
5x-6x^{2}-2+9
Combine -2x^{2} and -4x^{2} to get -6x^{2}.
5x-6x^{2}+7
Add -2 and 9 to get 7.
x-2x^{2}-2+4x-\left(2x-3\right)\left(2x+3\right)
Apply the distributive property by multiplying each term of x-2 by each term of 1-2x.
5x-2x^{2}-2-\left(2x-3\right)\left(2x+3\right)
Combine x and 4x to get 5x.
5x-2x^{2}-2-\left(\left(2x\right)^{2}-3^{2}\right)
Consider \left(2x-3\right)\left(2x+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
5x-2x^{2}-2-\left(2^{2}x^{2}-3^{2}\right)
Expand \left(2x\right)^{2}.
5x-2x^{2}-2-\left(4x^{2}-3^{2}\right)
Calculate 2 to the power of 2 and get 4.
5x-2x^{2}-2-\left(4x^{2}-9\right)
Calculate 3 to the power of 2 and get 9.
5x-2x^{2}-2-4x^{2}-\left(-9\right)
To find the opposite of 4x^{2}-9, find the opposite of each term.
5x-2x^{2}-2-4x^{2}+9
The opposite of -9 is 9.
5x-6x^{2}-2+9
Combine -2x^{2} and -4x^{2} to get -6x^{2}.
5x-6x^{2}+7
Add -2 and 9 to get 7.
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}