What is (x^2-1)^2+8x(x^2+1)+19x^2 ?

The solution to (x^2-1)^2+8x(x^2+1)+19x^2 is x^4+8x^3+17x^2+8x+1

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simplify (x^2-1)^2+8x(x^2+1)+19x^2

simplify

(x^{2} - 1)^{2} + 8 x (x^{2} + 1) + 19 x^{2}

x^{4} + 8 x^{3} + 17 x^{2} + 8 x + 1

Solution steps

(x^{2} - 1)^{2} + 8 x (x^{2} + 1) + 19 x^{2}

Expand

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

= x^{4} - 2 x^{2} + 1 + 8 x (x^{2} + 1) + 19 x^{2}

Expand

8 x (x^{2} + 1) : 8 x^{3} + 8 x

= x^{4} - 2 x^{2} + 1 + 8 x^{3} + 8 x + 19 x^{2}

Group like terms

= x^{4} + 8 x^{3} - 2 x^{2} + 19 x^{2} + 8 x + 1

Add similar elements:

- 2 x^{2} + 19 x^{2} = 17 x^{2}

= x^{4} + 8 x^{3} + 17 x^{2} + 8 x + 1

x^{2} + 2 x - \frac{2}{25} x - 2

4 x^{4} - 33 x^{2} + 8

289 x^{8} - y^{8}

x^{6} + 2 x + x^{2}

(a^{2})^{2} + (b^{2})^{2}

What is (x^2-1)^2+8x(x^2+1)+19x^2 ?
The solution to (x^2-1)^2+8x(x^2+1)+19x^2 is x^4+8x^3+17x^2+8x+1