Evaluate
-\left(x+2\right)\left(8x^{2}+45x+65\right)
Expand
-8x^{3}-61x^{2}-155x-130
Graph
Share
Copied to clipboard
-\left(8x^{3}+60x^{2}+150x+125\right)-\left(x+2\right)^{2}-\left(x+1\right)
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(2x+5\right)^{3}.
-8x^{3}-60x^{2}-150x-125-\left(x+2\right)^{2}-\left(x+1\right)
To find the opposite of 8x^{3}+60x^{2}+150x+125, find the opposite of each term.
-8x^{3}-60x^{2}-150x-125-\left(x^{2}+4x+4\right)-\left(x+1\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.
-8x^{3}-60x^{2}-150x-125-x^{2}-4x-4-\left(x+1\right)
To find the opposite of x^{2}+4x+4, find the opposite of each term.
-8x^{3}-61x^{2}-150x-125-4x-4-\left(x+1\right)
Combine -60x^{2} and -x^{2} to get -61x^{2}.
-8x^{3}-61x^{2}-154x-125-4-\left(x+1\right)
Combine -150x and -4x to get -154x.
-8x^{3}-61x^{2}-154x-129-\left(x+1\right)
Subtract 4 from -125 to get -129.
-8x^{3}-61x^{2}-154x-129-x-1
To find the opposite of x+1, find the opposite of each term.
-8x^{3}-61x^{2}-155x-129-1
Combine -154x and -x to get -155x.
-8x^{3}-61x^{2}-155x-130
Subtract 1 from -129 to get -130.
-\left(8x^{3}+60x^{2}+150x+125\right)-\left(x+2\right)^{2}-\left(x+1\right)
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(2x+5\right)^{3}.
-8x^{3}-60x^{2}-150x-125-\left(x+2\right)^{2}-\left(x+1\right)
To find the opposite of 8x^{3}+60x^{2}+150x+125, find the opposite of each term.
-8x^{3}-60x^{2}-150x-125-\left(x^{2}+4x+4\right)-\left(x+1\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.
-8x^{3}-60x^{2}-150x-125-x^{2}-4x-4-\left(x+1\right)
To find the opposite of x^{2}+4x+4, find the opposite of each term.
-8x^{3}-61x^{2}-150x-125-4x-4-\left(x+1\right)
Combine -60x^{2} and -x^{2} to get -61x^{2}.
-8x^{3}-61x^{2}-154x-125-4-\left(x+1\right)
Combine -150x and -4x to get -154x.
-8x^{3}-61x^{2}-154x-129-\left(x+1\right)
Subtract 4 from -125 to get -129.
-8x^{3}-61x^{2}-154x-129-x-1
To find the opposite of x+1, find the opposite of each term.
-8x^{3}-61x^{2}-155x-129-1
Combine -154x and -x to get -155x.
-8x^{3}-61x^{2}-155x-130
Subtract 1 from -129 to get -130.
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}