What is (y^2+1)^2-4(y^2+1) ?

The solution to (y^2+1)^2-4(y^2+1) is y^4-2y^2-3

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simplify (y^2+1)^2-4(y^2+1)

simplify

(y^{2} + 1)^{2} - 4 (y^{2} + 1)

y^{4} - 2 y^{2} - 3

Solution steps

(y^{2} + 1)^{2} - 4 (y^{2} + 1)

Expand

(y^{2} + 1)^{2} : y^{4} + 2 y^{2} + 1

= y^{4} + 2 y^{2} + 1 - 4 (y^{2} + 1)

Expand

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

= y^{4} + 2 y^{2} + 1 - 4 y^{2} - 4

Group like terms

= y^{4} + 2 y^{2} - 4 y^{2} + 1 - 4

Add similar elements:

2 y^{2} - 4 y^{2} = - 2 y^{2}

= y^{4} - 2 y^{2} + 1 - 4

Subtract the numbers:

1 - 4 = - 3

= y^{4} - 2 y^{2} - 3

- 5 (4)

- 5 + 18

3.5 \cdot 1 0^{1}

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