Multiplying and Distributing Radical Expressions - Problem 2

Here I’m going to use the distributive property, but it’s a little bit tricky because I’m distributing a radical expression. That’s square root of 3x has to be multiplied by the square root of 4x and also has to be multiplied by -5, so let’s go step by step.

Square root of 3x times square root of 4x is square root of 12x², don’t forget the x squared piece, and then square root of 3x times -5 I’m going to write like this. Next thing I need to do is simplify this piece here. Square root of 12 times the square root of x² because the square root of 12 can be broken down as the square root of 4 times the square root or 3 or 2 root 3. Then the square root of x² is just plain old x. So take away 5 square roots of 3x.

The last thing I’m going to do is rearrange this so it’s written properly. What we have is 2 times x, square roots of 3 take away 5 square roots of 3x. Be really careful these guys cannot be subtracted because they have different radicands. These are not like terms, so a lot of students will lose where there are Xs they’ll get confused by the placement of the Xs. This is the final answer. It looks pretty nasty, but this is the answer to that distributing problem.