How do you factor $a^2+4ab-3b^2$ ?

Question

3970 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-28T17:04:25

Complete the square to find:

$a^2+4ab-3b^2 = (a+(2-sqrt(7))b)(a+(2+sqrt(7))b)$

$(a+2b)^2 = a^2+4ab+4b^2$

So

$a^2 + 4ab - 3b^2$

$= (a+2b)^2 - 4b^2 - 3b^2$

$= (a+2b)^2 - 7b^2$

$= (a+2b)^2 - (sqrt(7)b)^2$

$= ((a+2b)-sqrt(7)b)((a+2b)+sqrt(7)b)$

$= (a+(2-sqrt(7))b)(a+(2+sqrt(7))b)$

...using the difference of squares identity

$A^2-B^2 = (A-B)(A+B)$

with $A=a+2b$ and $B=sqrt(7)b$

How do you factor a^2+4ab-3b^2 a^2+4ab-3b^2 ?