What is expand ((2x^2-6x+9)^2)/2 ?

The solution to expand ((2x^2-6x+9)^2)/2 is 2x^4-12x^3+36x^2-54x+81/2

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expand ((2x^2-6x+9)^2)/2

expand

\frac{( 2 x ^{2} - 6 x + 9 ) ^{2}}{2}

2 x^{4} - 12 x^{3} + 36 x^{2} - 54 x + \frac{81}{2}

Solution steps

\frac{( 2 x ^{2} - 6 x + 9 ) ^{2}}{2}

(2 x^{2} - 6 x + 9)^{2} = 4 x^{4} - 24 x^{3} + 72 x^{2} - 108 x + 81

= \frac{4 x ^{4} - 24 x ^{3} + 72 x ^{2} - 108 x + 81}{2}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{4 x ^{4} - 24 x ^{3} + 72 x ^{2} - 108 x + 81}{2} = \frac{4 x ^{4}}{2} - \frac{24 x ^{3}}{2} + \frac{72 x ^{2}}{2} - \frac{108 x}{2} + \frac{81}{2}

= \frac{4 x ^{4}}{2} - \frac{24 x ^{3}}{2} + \frac{72 x ^{2}}{2} - \frac{108 x}{2} + \frac{81}{2}

\frac{4 x ^{4}}{2} = 2 x^{4}

\frac{24 x ^{3}}{2} = 12 x^{3}

\frac{72 x ^{2}}{2} = 36 x^{2}

\frac{108 x}{2} = 54 x

= 2 x^{4} - 12 x^{3} + 36 x^{2} - 54 x + \frac{81}{2}

(35) (67)

(x^{2} y - x^{2} + y - 1) d y

(6 e + 7 z) (6 e - 7 z)

\frac{3 ( x + h ) + 4}{2 ( x + h ) - 9}

\frac{4 ( x + h ) + 7}{5 ( x + h ) - 6}

What is expand ((2x^2-6x+9)^2)/2 ?
The solution to expand ((2x^2-6x+9)^2)/2 is 2x^4-12x^3+36x^2-54x+81/2