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5.4 number 6.
Here we have a binomial and it is being squared.
So what we want to do is take the entire thing in
parentheses, multiply it by itself 2 times, because that's
what you do whenever you square something.
So we don't want to distribute the exponent in.
We need to do 3a plus 1/5 b times 3a plus 1/5 b.
So now we need to FOIL or distribute each term here onto
each term in the other binomial.
So we'll set up a work space on the left where we're going
to do our fraction scratch work.
And then here on the right, we will do our FOILing out.
So let's start with the 3a.
So 3a times 3a gives us 9a squared.
3a times 1/5 b--
let's just write that one out for now.
So we're done with 3a.
Now we go to 1/5 b times 3a.
And because they're being multiplied, I can put it in
either order, so I'm going to put in the same orders as the
one right before it.
3a times 1/5 b.
And then 1/5 b times 1/5 b.
And that's going to give me 1/25 b squared.
So first, let's take a look over on the side how 1/5 b
times 1/5 b gave us 1/25 b squared.
If have 1/5 b times 1/5 b, because everybody's being
multiplied together, I can go ahead and write 1/5 times 1/5.
I can rearrange the order.
Times b times b.
1/5 times 1/5, multiply across the top, across the bottom.
We get 1/25.
b times b is b squared.
And that's where this final term right
over here came from.
And now, let's take a look at how we can rewrite the 3a
times 1/5 b and combine those like terms.
So 3a times 1/5 b.
If you like to think of it as over 1, that makes it look
like a fraction multiplied by another fraction, so it's a
little bit nicer to see.
And think of this b as being part of this fraction right
here, or even think of it as over 1, also.
So now we have fractions being multiplied together.
So we multiply across the top, which gives us 3ab.
And then we have the 5 on the bottom.
Or in other words, 3/5 ab.
Now, we have two of those happening.
We have 3/5 ab plus 3/5 ab right over here.
So we want to combine those together.
And they have the same denominator already, so we
don't have to worry about that.
We're going to still have a 5 denominator.
3 plus 3 is 6, and then ab.
So 6/5 ab.
And that's how we can combine those middle terms.
So let's bring down the 9a squared, then the 3a times 1/5
b happening twice turns into 6/5 ab.
And then bring down the 1/25 b squared.
And that's how we have our final answer.