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-7x-30
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-7x-30
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x^{2}-4x-21-\left(x+3\right)^{2}+3x
Use the distributive property to multiply x-7 by x+3 and combine like terms.
x^{2}-4x-21-\left(x^{2}+6x+9\right)+3x
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.
x^{2}-4x-21-x^{2}-6x-9+3x
To find the opposite of x^{2}+6x+9, find the opposite of each term.
-4x-21-6x-9+3x
Combine x^{2} and -x^{2} to get 0.
-10x-21-9+3x
Combine -4x and -6x to get -10x.
-10x-30+3x
Subtract 9 from -21 to get -30.
-7x-30
Combine -10x and 3x to get -7x.
x^{2}-4x-21-\left(x+3\right)^{2}+3x
Use the distributive property to multiply x-7 by x+3 and combine like terms.
x^{2}-4x-21-\left(x^{2}+6x+9\right)+3x
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.
x^{2}-4x-21-x^{2}-6x-9+3x
To find the opposite of x^{2}+6x+9, find the opposite of each term.
-4x-21-6x-9+3x
Combine x^{2} and -x^{2} to get 0.
-10x-21-9+3x
Combine -4x and -6x to get -10x.
-10x-30+3x
Subtract 9 from -21 to get -30.
-7x-30
Combine -10x and 3x to get -7x.
Examples
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{ 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}