What is (a^2+1)^2+(a^2+5)^2-4*(a^2+3)^2 ?

The solution to (a^2+1)^2+(a^2+5)^2-4*(a^2+3)^2 is -2a^4-12a^2-10

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simplify (a^2+1)^2+(a^2+5)^2-4*(a^2+3)^2

simplify

(a^{2} + 1)^{2} + (a^{2} + 5)^{2} - 4 \cdot (a^{2} + 3)^{2}

- 2 a^{4} - 12 a^{2} - 10

Solution steps

(a^{2} + 1)^{2} + (a^{2} + 5)^{2} - 4 (a^{2} + 3)^{2}

Expand

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

= a^{4} + 2 a^{2} + 1 + (a^{2} + 5)^{2} - 4 (a^{2} + 3)^{2}

Expand

(a^{2} + 5)^{2} : a^{4} + 10 a^{2} + 25

= a^{4} + 2 a^{2} + 1 + a^{4} + 10 a^{2} + 25 - 4 (a^{2} + 3)^{2}

Expand

- 4 (a^{2} + 3)^{2} : - 4 a^{4} - 24 a^{2} - 36

= a^{4} + 2 a^{2} + 1 + a^{4} + 10 a^{2} + 25 - 4 a^{4} - 24 a^{2} - 36

Group like terms

= a^{4} + a^{4} - 4 a^{4} + 2 a^{2} + 10 a^{2} - 24 a^{2} + 1 + 25 - 36

Add similar elements:

a^{4} + a^{4} - 4 a^{4} = - 2 a^{4}

= - 2 a^{4} + 2 a^{2} + 10 a^{2} - 24 a^{2} + 1 + 25 - 36

Add similar elements:

2 a^{2} + 10 a^{2} - 24 a^{2} = - 12 a^{2}

= - 2 a^{4} - 12 a^{2} + 1 + 25 - 36

Add the numbers:

1 + 25 - 36 = - 10

= - 2 a^{4} - 12 a^{2} - 10

17 x^{3} + (3 x + 8 x^{3})

(14.5 - 5.3) \cdot x^{2.5} + (3.5) 2

\frac{( x ^{3} - 49 x )}{( x ^{4} - 7 x ^{3} )}

cos^{2} (x) sec^{2} (x)

512 x^{3} - 27 y^{3}

What is (a^2+1)^2+(a^2+5)^2-4*(a^2+3)^2 ?
The solution to (a^2+1)^2+(a^2+5)^2-4*(a^2+3)^2 is -2a^4-12a^2-10