Divide the following polynomials (a4 + 4b4) : (a2 - 2ab + 2b2)

(a^4 + 4b^4) : (a^2 - 2ab + 2b^2)

= [ (a^2 - 2ab + 2b^2) (a^2 + 2ab + 2b^2) ] / (a^2 - 2ab + 2b^2)

= a^2+2ab+2b^2 = The answer

(a + b) ^2 = a^2 + 2ab + b^2 = > square of sums

(a - b) ^2 = a^2 - 2ab + b^2 = > square of deference

and of course one of most important ones:

a^2 - b^2 = (a - b) (a + b) = > difference of squares

Best Answer: (a^4 + 4b^4) : (a^2 - 2ab + 2b^2)

= [ (a^2 - 2ab + 2b^2) (a^2 + 2ab + 2b^2) ] / (a^2 - 2ab + 2b^2)

= a^2 + 2ab + 2b^2

a^4 + 4b^4 = > i. e. 4a^2b^2,

a^4 + 4a^2b^2 + 4b^4 = > a^2 + 2ab + b^2 = (a + b) ^2, if : a = a^2, b = 2b^2:

(a^2 + 2b^2) ^2 = a^4 + 4a^2b^2 + 4b^4 = > We can't add or subtract the value to the expression.

a^4 + 4a^2b^2 + 4b^4 - 4a^2b^2 = >

(a^2 + 2b^2) ^2 - 4a^2b^2 = >

(a^2 + 2b^2 - 2ab) (a^2 + 2b^2 + 2ab) = >

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

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