Lesson video

Hi, my name is Mr. Clasper and today we're going to learn how to solve a quadratic equation by factorising.

Let's solve this equation.

In order to get a value of zero, that must mean that the total of the first bracket is equal to zero or the total of the second bracket is equal to zero.

So we're going to attempt to solve both of these equations.

So our first one is if Y plus seven is equal to zero, we can subtract seven from both sides, which means that Y is equal to negative seven.

And if we look at the second bracket and make that equal to zero, Y subtract two is equal to zero, and if we add two to both sides, this means that Y is equal to two, which would give the second bracket a total value of zero.

That means our two solutions are Y equals negative seven, and Y is also equal to two, as both of these values, substituted will give us a value of zero.

Here is a trickier example.

We need to factorise, Y squared minus seven Y minus 18 is equal to zero.

Our first job is to factorised this.

So using a multiplication grid, we're looking for two numbers that have a product of negative 18, and the sum of negative seven.

Those two numbers will be negative nine and positive two.

This means that our equation could also be written as Y plus two multiplied by Y minus nine is equal to zero as this is equivalent to our original expression on the left hand side.

Now we can solve as we did before.

So if Y plus two is equal to zero, we can subtract two from both sides, which means that Y is equal to negative two, and looking at our second bracket, if Y minus nine is equal to zero, adding nine to both sides would mean that we have a value of Y is equal to nine.

Therefore our two solutions are Y is equal to negative two, and Y is equal to nine.

Here's some questions for you to try.

Pause the video to complete your task and resume once you're finished.

And here are your answers.

If we look carefully at question two D, you can see that we only have one solution.

This is because when we factorise this, we get something which is called a perfect square.

So we will get X plus three and X plus three in both of our brackets.

And the final one, so two E, we get to solutions which are negative three and positive three.

This is because this is an example of a difference of two squares.

So when we factorise this, we will get X minus three and X plus three.

Here's another question for you to try.

Pause the video to complete your task and resume once you're finished.

And here are your answers.

So if we factorise, X squared plus four X plus four, we get a perfect square, which means that we have one solution.

And if we factorise X squared minus 36, that will give us X plus six and X minus six, which gives us two solutions.

Also, if you look at X squared plus 25, we cannot factorise that as there are no numbers which have a product of 25 and a sum of zero.

And that's it for today's lesson.

I hope you enjoyed it.

Hopefully see you soon.