SOLUTION: {{{ sqrt(3a)(sqrt(12a) - 2sqrt(8a^2)) }}} Does the {{{ sqrt(3a) }}} distribute to the {{{ 2 }}} factor in the 2nd term or to just the {{{ sqrt(8a^2) }}} factor? Either

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: {{{ sqrt(3a)(sqrt(12a) - 2sqrt(8a^2)) }}} Does the {{{ sqrt(3a) }}} distribute to the {{{ 2 }}} factor in the 2nd term or to just the {{{ sqrt(8a^2) }}} factor? Either       Log On


   

Question 1200110: +sqrt%283a%29%28sqrt%2812a%29+-+2sqrt%288a%5E2%29%29+
Does the +sqrt%283a%29+ distribute to the +2+ factor in the 2nd term or to just the
+sqrt%288a%5E2%29+ factor?
Either
+-6a%28sqrt%2824a%5E3%29%29+
or
+-2%28sqrt%2824a%5E3%29%29+ ???
Can you please give a complete explanation of this?
Thank you
jadams
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The sqrt%283a%29 distributes to each term inside the second factor!

Your first step can be
sqrt%283a%29%28sqrt%2812a%29+-+2sqrt%288a%5E2%29%29
sqrt%283a%29%2Asqrt%2812a%29-%28sqrt%283a%29%29%2A2sqrt%288a%5E2%29, which simply follows according to Distributive Property.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
+sqrt%283a%29%28sqrt%2812a%29+-+2sqrt%288a%5E2%29%29+

Does the +sqrt%283a%29+ distribute to the +2+ factor in the 2nd term or to just the +sqrt%288a%5E2%29+ factor?
Either   +-6a%28sqrt%2824a%5E3%29%29+
         or
         +-2%28sqrt%2824a%5E3%29%29+ ???

Can you please give a complete explanation of this?
Thank you
jadams

The sqrt%283a%29 is OUTSIDE of the parentheses, and sqrt%2812a%29+-+2sqrt%288a%5E2%29 is in the parentheses. Therefore, the sqrt%283a%29 MUST be 
distributed over the 2 monomials, matrix%281%2C3%2C+sqrt%2812a%29%2C+%22%2C+and%22%2C+-+2sqrt%288a%5E2%29%29 
We then get: sqrt%283a%29%28sqrt%2812a%29+-+2sqrt%288a%5E2%29%29
           
           

Put them together to get: