What is (4x-x^3+3)-(2x^2-3x^3+1) ?

The solution to (4x-x^3+3)-(2x^2-3x^3+1) is 2x^3-2x^2+4x+2

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simplify (4x-x^3+3)-(2x^2-3x^3+1)

simplify

(4 x - x^{3} + 3) - (2 x^{2} - 3 x^{3} + 1)

2 x^{3} - 2 x^{2} + 4 x + 2

Solution steps

(4 x - x^{3} + 3) - (2 x^{2} - 3 x^{3} + 1)

Apply rule:

(a) = a

(4 x - x^{3} + 3) = 4 x - x^{3} + 3

= 4 x - x^{3} + 3 - (2 x^{2} - 3 x^{3} + 1)

Apply the distributive law:

- (a - b) = - a + b

- (2 x^{2} - 3 x^{3} + 1) = - 2 x^{2} + 3 x^{3} - 1

= 4 x - x^{3} + 3 - 2 x^{2} + 3 x^{3} - 1

Group like terms

= - x^{3} + 3 x^{3} - 2 x^{2} + 4 x + 3 - 1

Add similar elements:

- x^{3} + 3 x^{3} = 2 x^{3}

= 2 x^{3} - 2 x^{2} + 4 x + 3 - 1

Subtract the numbers:

3 - 1 = 2

= 2 x^{3} - 2 x^{2} + 4 x + 2

\frac{8}{3 - 2}

- 77 + (- 46)

x^{2} + 9 x + \frac{81}{4}

3^{- 4} \cdot 3^{6}

38 \frac{1}{3} - 2 \frac{3}{5}

What is (4x-x^3+3)-(2x^2-3x^3+1) ?
The solution to (4x-x^3+3)-(2x^2-3x^3+1) is 2x^3-2x^2+4x+2