Steps to factorize a^4+4b^4

Question

anonymous · Answer

you can take a square like... $$(a^{2})^{2}+(2b ^{2})^{2}$$

anonymous · Answer

you have to complete the square

anonymous · Answer

1. what are the factors that will get you the answers?

a^2 * a^2 

and

2b^2 and 2b^2

2. Now, since there is no middle term and the terms are both positive, you know that it needs to be + * -.

Ergo

3. (a^2 + 2b^2) (a^2 - 2b^2)

anonymous · Answer

This pattern is also called the sum of two squares

mr.math · Answer

$$a^4+4b^4=(a^2)^2+(2b)^2+4a^2b^2-4a^2b^2=(a^2+2b^2)^2-4a^2b^2$$
$$=(a^2+2b^2)-(2ab)^2.$$
Use the difference between squares to factorize the above expression and you're done.

mr.math · Answer

Sorry typo, second line should be
$$=(a^2+2b^2)^2-(2ab)^2.$$

mr.math · Answer

@dreamergurl your answer would be correct if the expression was $a^4-4b^4$.

anonymous · Answer

ugh you're right. Thanks, Mr. Math.

anonymous · Answer

Wait, how did you get my name to turn blue?

mr.math · Answer

I just added "@" before it as you can see :-)

mr.math · Answer

Nice picture and nice name by the way.