What is (6-2x-x^2)^2-(x+6)^2 ?

The solution to (6-2x-x^2)^2-(x+6)^2 is x^4+4x^3-9x^2-36x

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simplify (6-2x-x^2)^2-(x+6)^2

simplify

(6 - 2 x - x^{2})^{2} - (x + 6)^{2}

x^{4} + 4 x^{3} - 9 x^{2} - 36 x

Solution steps

(6 - 2 x - x^{2})^{2} - (x + 6)^{2}

Expand

(6 - 2 x - x^{2})^{2} : x^{4} + 4 x^{3} - 8 x^{2} - 24 x + 36

= x^{4} + 4 x^{3} - 8 x^{2} - 24 x + 36 - (x + 6)^{2}

Expand

- (x + 6)^{2} : - x^{2} - 12 x - 36

= x^{4} + 4 x^{3} - 8 x^{2} - 24 x + 36 - x^{2} - 12 x - 36

Group like terms

= x^{4} + 4 x^{3} - 8 x^{2} - x^{2} - 24 x - 12 x + 36 - 36

Add similar elements:

- 8 x^{2} - x^{2} = - 9 x^{2}

= x^{4} + 4 x^{3} - 9 x^{2} - 24 x - 12 x + 36 - 36

Add similar elements:

- 24 x - 12 x = - 36 x

= x^{4} + 4 x^{3} - 9 x^{2} - 36 x + 36 - 36

Subtract the numbers:

36 - 36 = 0

= x^{4} + 4 x^{3} - 9 x^{2} - 36 x

(\frac{4}{5} x - 1)^{2}

(4 x^{2} + 2 x - 5) + (6 x^{2} - x - 5)

(a - 1) (b - 1)

6 m^{2} n - m n^{2}

(\frac{4 k ^{6}}{2 k ^{2}})^{4}

What is (6-2x-x^2)^2-(x+6)^2 ?
The solution to (6-2x-x^2)^2-(x+6)^2 is x^4+4x^3-9x^2-36x