Question

Factor the expression c^2+4c-4

Answer 1

`Method\ 1^o\\Use\ a^2+2ab+b^2=(a+b)^2\\\\c^2+4c-4=0\ \ \ |add\ 8\ to\ both\ sides\\\\c^2+2c\cdot2+4=8\\\\c^2+2c\cdot2+2^2=8\\\\(c+2)^2=8\iff c+2=-\sqrt8\ or\ c+2=\sqrt8\\\\/\sqrt8=√(4\cdot2)=\sqrt4\cdot\sqrt2=2\sqrt2/\\\\c+2=-2\sqrt2\ or\ c+2=2\sqrt2\ \ \ |subtract\ 2\ from\ both\ sides\\\\\boxed{c=-2\sqrt2-2\ or\ c=2\sqrt2-2}`


`Method\ 2^o:\\change\`