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-10x^{3}-57x^{2}-70x-24
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-10x^{3}-57x^{2}-70x-24
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8x^{3}+12x^{2}+10x+1-\left(9x^{2}+30x+25\right)\left(2x+1\right)
Multiply 3 and 4 to get 12.
8x^{3}+12x^{2}+10x+1-\left(18x^{3}+69x^{2}+80x+25\right)
Use the distributive property to multiply 9x^{2}+30x+25 by 2x+1 and combine like terms.
8x^{3}+12x^{2}+10x+1-18x^{3}-69x^{2}-80x-25
To find the opposite of 18x^{3}+69x^{2}+80x+25, find the opposite of each term.
-10x^{3}+12x^{2}+10x+1-69x^{2}-80x-25
Combine 8x^{3} and -18x^{3} to get -10x^{3}.
-10x^{3}-57x^{2}+10x+1-80x-25
Combine 12x^{2} and -69x^{2} to get -57x^{2}.
-10x^{3}-57x^{2}-70x+1-25
Combine 10x and -80x to get -70x.
-10x^{3}-57x^{2}-70x-24
Subtract 25 from 1 to get -24.
8x^{3}+12x^{2}+10x+1-\left(9x^{2}+30x+25\right)\left(2x+1\right)
Multiply 3 and 4 to get 12.
8x^{3}+12x^{2}+10x+1-\left(18x^{3}+69x^{2}+80x+25\right)
Use the distributive property to multiply 9x^{2}+30x+25 by 2x+1 and combine like terms.
8x^{3}+12x^{2}+10x+1-18x^{3}-69x^{2}-80x-25
To find the opposite of 18x^{3}+69x^{2}+80x+25, find the opposite of each term.
-10x^{3}+12x^{2}+10x+1-69x^{2}-80x-25
Combine 8x^{3} and -18x^{3} to get -10x^{3}.
-10x^{3}-57x^{2}+10x+1-80x-25
Combine 12x^{2} and -69x^{2} to get -57x^{2}.
-10x^{3}-57x^{2}-70x+1-25
Combine 10x and -80x to get -70x.
-10x^{3}-57x^{2}-70x-24
Subtract 25 from 1 to get -24.
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Limits
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