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3x^{2}+x-3x-1-\left(x+1\right)
Apply the distributive property by multiplying each term of x-1 by each term of 3x+1.
3x^{2}-2x-1-\left(x+1\right)
Combine x and -3x to get -2x.
3x^{2}-2x-1-x-1
To find the opposite of x+1, find the opposite of each term.
3x^{2}-3x-1-1
Combine -2x and -x to get -3x.
3x^{2}-3x-2
Subtract 1 from -1 to get -2.
3x^{2}+x-3x-1-\left(x+1\right)
Apply the distributive property by multiplying each term of x-1 by each term of 3x+1.
3x^{2}-2x-1-\left(x+1\right)
Combine x and -3x to get -2x.
3x^{2}-2x-1-x-1
To find the opposite of x+1, find the opposite of each term.
3x^{2}-3x-1-1
Combine -2x and -x to get -3x.
3x^{2}-3x-2
Subtract 1 from -1 to get -2.