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

The solution to (x^2-1)^2+6(x^2-1) is x^4+4x^2-5

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simplify (x^2-1)^2+6(x^2-1)

simplify

(x^{2} - 1)^{2} + 6 (x^{2} - 1)

x^{4} + 4 x^{2} - 5

Solution steps

(x^{2} - 1)^{2} + 6 (x^{2} - 1)

Expand

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

= x^{4} - 2 x^{2} + 1 + 6 (x^{2} - 1)

Expand

6 (x^{2} - 1) : 6 x^{2} - 6

= x^{4} - 2 x^{2} + 1 + 6 x^{2} - 6

Group like terms

= x^{4} - 2 x^{2} + 6 x^{2} + 1 - 6

Add similar elements:

- 2 x^{2} + 6 x^{2} = 4 x^{2}

= x^{4} + 4 x^{2} + 1 - 6

Subtract the numbers:

1 - 6 = - 5

= x^{4} + 4 x^{2} - 5

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\frac{6 ^{8} 4 ^{9} m}{6 ^{6} 4 ^{8} m}

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