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

The solution to expand 2(x^2-2x+3)^3 is 2x^6-12x^5+42x^4-88x^3+126x^2-108x+54

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

expand

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

2 x^{6} - 12 x^{5} + 42 x^{4} - 88 x^{3} + 126 x^{2} - 108 x + 54

Solution steps

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

(x^{2} - 2 x + 3)^{3} = x^{6} - 6 x^{5} + 21 x^{4} - 44 x^{3} + 63 x^{2} - 54 x + 27

= 2 (x^{6} - 6 x^{5} + 21 x^{4} - 44 x^{3} + 63 x^{2} - 54 x + 27)

Distribute parentheses

= 2 x^{6} + 2 (- 6 x^{5}) + 2 \cdot 21 x^{4} + 2 (- 44 x^{3}) + 2 \cdot 63 x^{2} + 2 (- 54 x) + 2 \cdot 27

Apply minus-plus rules

+ (- a) = - a

= 2 x^{6} - 2 \cdot 6 x^{5} + 2 \cdot 21 x^{4} - 2 \cdot 44 x^{3} + 2 \cdot 63 x^{2} - 2 \cdot 54 x + 2 \cdot 27

Simplify

2 x^{6} - 2 \cdot 6 x^{5} + 2 \cdot 21 x^{4} - 2 \cdot 44 x^{3} + 2 \cdot 63 x^{2} - 2 \cdot 54 x + 2 \cdot 27 : 2 x^{6} - 12 x^{5} + 42 x^{4} - 88 x^{3} + 126 x^{2} - 108 x + 54

= 2 x^{6} - 12 x^{5} + 42 x^{4} - 88 x^{3} + 126 x^{2} - 108 x + 54

(e^{n + 1} - e^{n}) e^{n}

- 3 (4 x + 3) + 4 (6 x + 1 = 43)

(x + 1) d y + (y - 1) d x

(e^{- 2 t} - e^{- t})^{2}

\frac{1}{s ^{2} ( s + 5 ) ( s + 1 )}

What is expand 2(x^2-2x+3)^3 ?
The solution to expand 2(x^2-2x+3)^3 is 2x^6-12x^5+42x^4-88x^3+126x^2-108x+54