Simplify each expression by collecting and combining like terms.
$3 x^{2} - x + 1 + 3 x^{2} - 5 x^{3} + 2 + 4 x - 3 x^{2} + x^{3}$

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Solution

Simplify the polynomials.
Given, polynomials is $3 x^{2} - x + 1 + 3 x^{2} - 5 x^{3} + 2 + 4 x - 3 x^{2} + x^{3}$
Rearrange the like terms and add them with using a distributive law.
$3 x^{2} - x + 1 + 3 x^{2} - 5 x^{3} + 2 + 4 x - 3 x^{2} + x^{3} = - 5 x^{3} + x^{3} + 3 x^{2} + 3 x^{2} - 3 x^{2} - x + 4 x + 1 + 2 = (- 5 + 1) x^{3} + (3 + 3 - 3) x^{2} + (- 1 + 4) x + 3 = - 4 x^{3} + 3 x^{2} + 3 x + 3$
Hence, on simplifying $3 x^{2} - x + 1 + 3 x^{2} - 5 x^{3} + 2 + 4 x - 3 x^{2} + x^{3}$ , we get $- 4 x^{3} + 3 x^{2} + 3 x + 3$ .

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