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-3x-5
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-3x-5
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x^{2}+2x+1-\left(x+2\right)\left(x+3\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
x^{2}+2x+1-\left(x^{2}+5x+6\right)
Use the distributive property to multiply x+2 by x+3 and combine like terms.
x^{2}+2x+1-x^{2}-5x-6
To find the opposite of x^{2}+5x+6, find the opposite of each term.
2x+1-5x-6
Combine x^{2} and -x^{2} to get 0.
-3x+1-6
Combine 2x and -5x to get -3x.
-3x-5
Subtract 6 from 1 to get -5.
x^{2}+2x+1-\left(x+2\right)\left(x+3\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
x^{2}+2x+1-\left(x^{2}+5x+6\right)
Use the distributive property to multiply x+2 by x+3 and combine like terms.
x^{2}+2x+1-x^{2}-5x-6
To find the opposite of x^{2}+5x+6, find the opposite of each term.
2x+1-5x-6
Combine x^{2} and -x^{2} to get 0.
-3x+1-6
Combine 2x and -5x to get -3x.
-3x-5
Subtract 6 from 1 to get -5.
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}