WEBVTT

00:00:00.500 --> 00:00:03.868
Welcome to GCSE Edexcel Maths revision.

00:00:04.018 --> 00:00:07.075
Topic M 8: Expanding and factorising.

00:00:07.225 --> 00:00:09.401
This video covers Higher tier.

00:00:09.551 --> 00:00:13.541
It includes the shared content and the labelled Higher extensions.

00:00:16.200 --> 00:00:25.425
Distribute the term outside a bracket to every term inside: 3 multiplied by open bracket x plus 4 close bracket equals 3 x plus 12.

00:00:25.575 --> 00:00:34.203
A minus sign outside changes every sign: minus open bracket 2 x minus 5 close bracket equals minus 2 x plus 5.

00:00:36.867 --> 00:00:52.236
Worked example: 4 multiplied by open bracket 2 x minus 3 close bracket minus 2 multiplied by open bracket x plus 5 close bracket equals 8 x minus 12 minus 2 x minus 10 equals 6 x minus 22.

00:00:52.386 --> 00:00:54.892
Expand before collecting like terms.

00:00:57.567 --> 00:00:59.039
For two brackets,

00:00:59.189 --> 00:01:14.825
multiply every term in one by every term in the other. open bracket x plus 3 close bracket multiplied by open bracket x plus 2 close bracket equals x squared plus 2 x plus 3 x plus 6 equals x squared plus 5 x plus 6.

00:01:14.975 --> 00:01:17.557
Area model for expanding two brackets

00:01:22.233 --> 00:01:35.661
Useful identities are open bracket a plus b close bracket squared equals a squared plus 2 a b plus b squared and open bracket a minus b close bracket squared equals a squared minus 2 a b plus b squared .

00:01:35.811 --> 00:01:37.667
The middle term is essential.

00:01:40.333 --> 00:01:42.765
Factorising reverses expanding.

00:01:42.915 --> 00:01:51.565
Take out the highest common factor: 12 x squared plus 8 x equals 4 x multiplied by open bracket 3 x plus 2 close bracket .

00:01:51.715 --> 00:01:54.083
Expanding again checks both terms.

00:01:56.733 --> 00:01:59.677
To factorise x squared plus b x plus c,

00:01:59.827 --> 00:02:11.805
find two numbers whose sum is b and product is c. x squared plus 7 x plus 12 equals open bracket x plus 3 close bracket multiplied by open bracket x plus 4 close bracket .

00:02:14.467 --> 00:02:24.405
Worked example: x squared minus x minus 12 equals open bracket x minus 4 close bracket multiplied by open bracket x plus 3 close bracket ,

00:02:24.555 --> 00:02:32.768
because minus 4 plus 3 equals minus 1 and open bracket minus 4 close bracket multiplied by 3 equals minus 12.

00:02:35.433 --> 00:02:45.522
A difference of two squares is a squared minus b squared equals open bracket a minus b close bracket multiplied by open bracket a plus b close bracket .

00:02:45.672 --> 00:02:54.950
Thus x squared minus 25 equals open bracket x minus 5 close bracket multiplied by open bracket x plus 5 close bracket .

00:02:55.100 --> 00:02:57.798
A sum of squares does not use this identity.

00:03:00.467 --> 00:03:04.015
Factorising an expression does not by itself find x.

00:03:04.165 --> 00:03:09.285
To solve an equation, first make one side zero, then use the zero-product rule.

00:03:11.967 --> 00:03:20.818
For a x squared plus b x plus c with a is not equal to 1, find a factorisation that produces both the correct leading coefficient and middle term.

00:03:23.500 --> 00:03:47.071
Worked example: 6 x squared plus 7 x plus 2 equals 6 x squared plus 3 x plus 4 x plus 2 equals 3 x multiplied by open bracket 2 x plus 1 close bracket plus 2 multiplied by open bracket 2 x plus 1 close bracket equals open bracket 3 x plus 2 close bracket multiplied by open bracket 2 x plus 1 close bracket .

00:03:49.733 --> 00:03:51.312
For three brackets,

00:03:51.462 --> 00:03:52.806
expand two,

00:03:52.956 --> 00:03:54.193
simplify,

00:03:54.343 --> 00:04:16.741
then multiply the result by the third. open bracket x plus 1 close bracket multiplied by open bracket x minus 1 close bracket multiplied by open bracket x plus 2 close bracket equals open bracket x squared minus 1 close bracket multiplied by open bracket x plus 2 close bracket equals x cubed plus 2 x squared minus x minus 2.

00:04:19.400 --> 00:04:36.273
Look for a common factor before a quadratic pattern: 2 x squared minus 18 equals 2 open bracket x squared minus 9 close bracket equals 2 multiplied by open bracket x minus 3 close bracket multiplied by open bracket x plus 3 close bracket .

00:04:38.933 --> 00:04:41.515
That completes Expanding and factorising.

00:04:41.665 --> 00:04:45.010
Revisit the notes and test yourself on the revision website.