Type a math problem
Evaluate
Solution Steps
Use the distributive property to multiply by .
Apply the distributive property by multiplying each term of by each term of .
Combine and to get .
To find the opposite of , find the opposite of each term.
The opposite of is .
The opposite of is .
Combine and to get .
Expand
Solution Steps
Use the distributive property to multiply by .
Apply the distributive property by multiplying each term of by each term of .
Combine and to get .
To find the opposite of , find the opposite of each term.
The opposite of is .
The opposite of is .
Combine and to get .
Factor
Solution Steps
Factor out common term by using distributive property.
Consider . Simplify.
Factor the expression by grouping. First, the expression needs to be rewritten as . To find and , set up a system to be solved.
Since is negative, and have the opposite signs. Since is positive, the positive number has greater absolute value than the negative. The only such pair is the system solution.
Rewrite as .
Factor out in the first and in the second group.
Factor out common term by using distributive property.
Rewrite the complete factored expression.
Graph
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-5x-\left(x^{2}+2x\right)\left(x-4\right)
Use the distributive property to multiply x by x+2.
-5x-\left(x^{3}-4x^{2}+2x^{2}-8x\right)
Apply the distributive property by multiplying each term of x^{2}+2x by each term of x-4.
-5x-\left(x^{3}-2x^{2}-8x\right)
Combine -4x^{2} and 2x^{2} to get -2x^{2}.
-5x-x^{3}-\left(-2x^{2}\right)-\left(-8x\right)
To find the opposite of x^{3}-2x^{2}-8x, find the opposite of each term.
-5x-x^{3}+2x^{2}-\left(-8x\right)
The opposite of -2x^{2} is 2x^{2}.
-5x-x^{3}+2x^{2}+8x
The opposite of -8x is 8x.
3x-x^{3}+2x^{2}
Combine -5x and 8x to get 3x.
-5x-\left(x^{2}+2x\right)\left(x-4\right)
Use the distributive property to multiply x by x+2.
-5x-\left(x^{3}-4x^{2}+2x^{2}-8x\right)
Apply the distributive property by multiplying each term of x^{2}+2x by each term of x-4.
-5x-\left(x^{3}-2x^{2}-8x\right)
Combine -4x^{2} and 2x^{2} to get -2x^{2}.
-5x-x^{3}-\left(-2x^{2}\right)-\left(-8x\right)
To find the opposite of x^{3}-2x^{2}-8x, find the opposite of each term.
-5x-x^{3}+2x^{2}-\left(-8x\right)
The opposite of -2x^{2} is 2x^{2}.
-5x-x^{3}+2x^{2}+8x
The opposite of -8x is 8x.
3x-x^{3}+2x^{2}
Combine -5x and 8x to get 3x.
x\left(-\left(x+2\right)\left(x-4\right)-5\right)
Factor out common term x by using distributive property.
-x^{2}+2x+3
Consider -\left(x+2\right)\left(x-4\right)-5. Simplify.
a+b=2 ab=-3=-3
Factor the expression by grouping. First, the expression needs to be rewritten as -x^{2}+ax+bx+3. To find a and b, set up a system to be solved.
a=3 b=-1
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. The only such pair is the system solution.
\left(-x^{2}+3x\right)+\left(-x+3\right)
Rewrite -x^{2}+2x+3 as \left(-x^{2}+3x\right)+\left(-x+3\right).
-x\left(x-3\right)-\left(x-3\right)
Factor out -x in the first and -1 in the second group.
\left(x-3\right)\left(-x-1\right)
Factor out common term x-3 by using distributive property.
x\left(x-3\right)\left(-x-1\right)
Rewrite the complete factored expression.