Divide the following polynomials (a4 + 4b4) ÷ (a2 - 2ab + 2b2)
2 answers:
(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) Greetings!
Answer:
(a^2+2ab+2b^2)
Step-by-step explanation:
(a^4 + 4b^4) ÷ (a^2 - 2ab + 2b^2)
To factor a^4 - 4b^4 we use square form
subtract 4a^2 b^2 on both sides
---------> equation we got
Now apply difference of square formula
x^2- y^2 = (x+y)(x-y)
Replace the factors in the equation we got
Now replace it in our original equation
Cancel out same factors
So answer is
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