What is expand 4x(2x^2-1+ce^{-2x^2}) ?

The solution to expand 4x(2x^2-1+ce^{-2x^2}) is 8x^3-4x+4ce^{-2x^2}x

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expand 4x(2x^2-1+ce^{-2x^2})

expand

4 x (2 x^{2} - 1 + c e^{- 2 x^{2}})

8 x^{3} - 4 x + 4 c e^{- 2 x^{2}} x

Solution steps

4 x (2 x^{2} - 1 + c e^{- 2 x^{2}})

Distribute parentheses

= 4 x \cdot 2 x^{2} + 4 x (- 1) + 4 x c e^{- 2 x^{2}}

Apply minus-plus rules

+ (- a) = - a

= 4 \cdot 2 x^{2} x - 4 \cdot 1 \cdot x + 4 c e^{- 2 x^{2}} x

Simplify

4 \cdot 2 x^{2} x - 4 \cdot 1 \cdot x + 4 c e^{- 2 x^{2}} x : 8 x^{3} - 4 x + 4 c e^{- 2 x^{2}} x

= 8 x^{3} - 4 x + 4 c e^{- 2 x^{2}} x

a (2, - 3) b (4, 2) c (4, - 3)

(1 + c e^{- x})^{2}

\frac{1}{( x + 4 ) ( x - 2 )}

\frac{1}{( x + 1 ) ( 3 x + 1 ) ( 6 x + 3 )}

\frac{8 x ^{2} + 12 x}{( 3 x - 2 ) ^{2}}

What is expand 4x(2x^2-1+ce^{-2x^2}) ?
The solution to expand 4x(2x^2-1+ce^{-2x^2}) is 8x^3-4x+4ce^{-2x^2}x