Proof that: $\displaystyle sqrt(ab-ac)=asqrt(b-c)$
without the use of substitution
Thx
As Prove It said, you can't prove that- it's not true.
Did you mean $\displaystyle \sqrt{a^2b- a^2c}= a\sqrt{b- c}$?
(assuming that a is non-negative)
I'm not sure what you mean by "without the use of substitution"- I see nothing to substitute there- but
$\displaystyle \sqrt{a^2b- a^2c}= \sqrt{a^2(b- c)}= \sqrt{a^2}\sqrt{b- c}= a\sqrt{b- c}$
($\displaystyle \sqrt{a^2}= a$ if a is non-negative. $\displaystyle \sqrt{a^2}= -a$ if a is negative.)