Question

a^4 + 9b^4 + 2*a^2*b^2

Answer 1

Answer:

Enter a problem...

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Basic Math

 

Factor a^4+2a^2b^2+9b^4

a4+2a2b2+9b4a4+2a2b2+9b4

Rewrite the middle term.

a4+2a2(3b2)−4a2b2+9b4a4+2a2(3b2)-4a2b2+9b4

Rearrange terms.

a4+2a2(3b2)+9b4−4a2b2a4+2a2(3b2)+9b4-4a2b2

Factor first three terms by perfect square rule.

(a2+3b2)2−4a2b2(a2+3b2)2-4a2b2

Rewrite 4a2b24a2b2 as (2ab)2(2ab)2.

(a2+3b2)2−(2ab)2(a2+3b2)2-(2ab)2

Since both terms are perfect squares, factor using the difference of squares formula, a2−b2=(a+b)(a−b)a2-b2=(a+b)(a-b)where a=a2+3b2a=a2+3b2 and b=2abb=2ab.

(a2+3b2+2ab)(a2+3b2−(2ab))

Multiply 22 by −1-1.

(a2+3b2+2ab)(a2+3b2−2(ab))(a2+3b2+2ab)(a2+3b2-2(ab))

Remove parentheses.

(a2+3b2+2ab)(a2+3b2−2ab)

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Answer 2

Answer:

(a^2 +3b^2 + 2ab)(a^2+3b^2 - 2ab)