What is expand (9-1/2 x^2)^2-(x^2-6x+9)^2 ?

The solution to expand (9-1/2 x^2)^2-(x^2-6x+9)^2 is (-3x^4-252x^2+324)/4+12x^3+108x-81

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expand (9-1/2 x^2)^2-(x^2-6x+9)^2

expand

(9 - \frac{1}{2} x^{2})^{2} - (x^{2} - 6 x + 9)^{2}

\frac{- 3 x ^{4} - 252 x ^{2} + 324}{4} + 12 x^{3} + 108 x - 81

Solution steps

(9 - \frac{1}{2} x^{2})^{2} - (x^{2} - 6 x + 9)^{2}

Expand

(9 - \frac{1}{2} x^{2})^{2} : \frac{324 - 36 x ^{2} + x ^{4}}{4}

= \frac{324 - 36 x ^{2} + x ^{4}}{4} - (x^{2} - 6 x + 9)^{2}

Expand

- (x^{2} - 6 x + 9)^{2} : - x^{4} + 12 x^{3} - 54 x^{2} + 108 x - 81

= \frac{324 - 36 x ^{2} + x ^{4}}{4} - x^{4} + 12 x^{3} - 54 x^{2} + 108 x - 81

Join

\frac{324 - 36 x ^{2} + x ^{4}}{4} - x^{4} + 12 x^{3} - 54 x^{2} + 108 x - 81 : \frac{- 3 x ^{4} - 252 x ^{2} + 324}{4} + 12 x^{3} + 108 x - 81

= \frac{- 3 x ^{4} - 252 x ^{2} + 324}{4} + 12 x^{3} + 108 x - 81

(7 - 6) 2

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

f (5 x^{5} - 2 x^{4} + 3 x^{3} + 5 x^{2} + 2 e + 5) d x

\frac{2 ( 65 65 - 1 )}{3}

(z + i 2)^{2}

What is expand (9-1/2 x^2)^2-(x^2-6x+9)^2 ?
The solution to expand (9-1/2 x^2)^2-(x^2-6x+9)^2 is (-3x^4-252x^2+324)/4+12x^3+108x-81