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