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8. Simplify: (-5x^2+x^3-2x+3)-(-5x^2-x^3+3x+1) A. 2x+4 B 2x^3-6x-5 C 2x^3-5x+2 D 2x^3-10x^2+5x+4

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8. Simplify: (-5x^2+x^3-2x+3)-(-5x^2-x^3+3x+1) A. 2x+4 B 2x^3-6x-5 C 2x^3-5x+2 D 2x^3-10x^2+5x+4

8. Simplify: (-5x^2+x^3-2x+3)-(-5x^2-x^3+3x+1) A. 2x+4 B 2x^3-6x-5 C 2x^3-5x+2 D 2x^3-10x^2+5x+4

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YancyMaster · Tutor for 5 years

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To simplify the expression, we distribute the negative sign to the terms inside the second set of parentheses and then combine like terms:\(\left(-5 x^{2}+x^{3}-2 x+3\right)-\left(-5 x^{2}-x^{3}+3 x+1\right)\)Becomes:\(-5 x^{2}+x^{3}-2 x+3+5 x^{2}+x^{3}-3 x-1\)Combine like terms:\((x^{3}+x^{3})+(-5 x^{2}+5 x^{2})+(-2 x-3 x)+(3-1)\)\(2 x^{3}+0 x^{2}-5 x+2\)The simplified expression is:\(2 x^{3}-5 x+2\)The correct answer is C. \(2 x^{3}-5 x+2\)
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