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Hello, everyone.

This lesson concerns expanding double brackets with Surds.

Hi, everyone.

Let's expand and simplify these double brackets containing Surds.

I'm going to use grid method to help me.

Take the first bracket and place each term alongside the grid like so.

Take the second bracket, place each term alongside the grid like this, then, find the product of each corresponding term.

Here are the results.

Write out your results like so, and then collect your like terms and simplify.

That gives you an answer of 16, lots of the square root two plus 65.

What do you think that is as a decimal number? Put it in the calculator and save.

Let's have a look at a second example.

What's different with this example? I see a negative sign in the first bracket.

We must be careful when multiplying negative signs.

Here's our multiplication grid.

I've tried to emphasise the difference between the negative and the positive terms and there we go, if I multiply each corresponding term together, those are the products.

Notice down in the bottom right hand corner I can simplify this result to give me negative 12, lots of the square root of two.

You don't have to do it at this stage, but at some point you will have to simplify.

So why not do it now? Let's write all of those terms in a line.

And then let's collect our terms to simplify, to give us negative nine, lots of the square two plus 14.

You could also write that as 14 minus nine, lots of the squared two.

Okay.

Here's some examples for you to try, pause the video and return to check your answers.

Here are the solutions to questions number one.

Some people like to use the foil method.

I particular like the grid method for this particular skill.

Either is fine.

Here's some more examples for you to try, use the grid method to help you.

If you prefer foil method, that's fine, as long as you're getting the right results.

Pause the video and return to check your answers.

Here are the solutions to questions number two.

How did you do? Did you notice that in questions, A, B, C, and D the Surds are the same in both brackets? But in question E we have two different Surds.

How did that affect your working out and the results that you found? Give it a think.

Here's some more questions for you to try.

Pause video and return to check your answers.

Here are the solutions to questions number three.

If I am expanding and simplifying something slightly more complicated with a few more algebraic terms, then, use the Greek method, it does help.

Well done for getting this far, pause the video, return to check your answers.

Here's the solutions to questions number four.

Well done for getting this far.

Working with Surds is never easy.

There's a lot to think about.

Nevertheless, if you work methodically, you should find the right answers.

Well done.