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

The solution to expand 4(3x^2+3x-1)^3 is 108x^6+324x^5+216x^4-108x^3-72x^2+36x-4

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

expand

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

108 x^{6} + 324 x^{5} + 216 x^{4} - 108 x^{3} - 72 x^{2} + 36 x - 4

Solution steps

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

(3 x^{2} + 3 x - 1)^{3} = 27 x^{6} + 81 x^{5} + 54 x^{4} - 27 x^{3} - 18 x^{2} + 9 x - 1

= 4 (27 x^{6} + 81 x^{5} + 54 x^{4} - 27 x^{3} - 18 x^{2} + 9 x - 1)

Distribute parentheses

= 4 \cdot 27 x^{6} + 4 \cdot 81 x^{5} + 4 \cdot 54 x^{4} + 4 (- 27 x^{3}) + 4 (- 18 x^{2}) + 4 \cdot 9 x + 4 (- 1)

Apply minus-plus rules

+ (- a) = - a

= 4 \cdot 27 x^{6} + 4 \cdot 81 x^{5} + 4 \cdot 54 x^{4} - 4 \cdot 27 x^{3} - 4 \cdot 18 x^{2} + 4 \cdot 9 x - 4 \cdot 1

Simplify

4 \cdot 27 x^{6} + 4 \cdot 81 x^{5} + 4 \cdot 54 x^{4} - 4 \cdot 27 x^{3} - 4 \cdot 18 x^{2} + 4 \cdot 9 x - 4 \cdot 1 : 108 x^{6} + 324 x^{5} + 216 x^{4} - 108 x^{3} - 72 x^{2} + 36 x - 4

= 108 x^{6} + 324 x^{5} + 216 x^{4} - 108 x^{3} - 72 x^{2} + 36 x - 4

x (1 - x)

(8 x - 3) (3 x - 3)

\frac{18 ( 216 n ^{2} - 162 n - 54 )}{n ^{2}}

\frac{d}{d x} ((2) (a x e^{- 2 x} + 6))

\frac{e ^{- s}}{s ^{3} ( s ^{2} + 1 )}

What is expand 4(3x^2+3x-1)^3 ?
The solution to expand 4(3x^2+3x-1)^3 is 108x^6+324x^5+216x^4-108x^3-72x^2+36x-4