Expanding, Factorising and Proof: Where to start

X squared plus five x plus six, and the bracket x plus two times the bracket x plus three, are one expression written two ways. Expanding opens the brackets out into the long form. Factorising packs it back into brackets. This chapter is those two jobs, and the proofs they make possible. Here is where to put your time, and which video to open first.

The whole chapter is on your screen. The videos build on one another, with the factorising ones leaning on expanding.

Expanding a Single Bracket is the place to begin if brackets are new or shaky. Common slips are losing the negative outside the bracket, and multiplying only the first term inside. Expanding Double Brackets is the one most of the chapter leans on. Students tend to know the method, then slip when they combine the middle terms. Expanding Three or More Brackets comes next, on the Higher tier, and runs that same method twice. Factorising by Taking Out a Common Factor is where to go next if expanding already feels solid. Common slips are stopping with only part of the factor out, or reaching for two brackets when one is enough. Factorising a Quadratic, Including Difference of Two Squares covers the standard quadratic and a pattern most students miss, so they hunt for factor pairs that are not there. Factorising a General Quadratic is for when the number in front of x squared is not one, and it is Higher only. It gives you a step-by-step method in place of guessing brackets. Completing the Square is Higher as well. It rewrites a quadratic as a squared bracket, plus or minus a number. Simplifying and Manipulating Algebraic Fractions is Higher only. A common slip is cancelling single terms, when only whole factors can be cancelled. Equations, Identities and Equivalent Expressions is the way into the proof side of the chapter. Very few students know how to find the missing numbers in an identity by matching its two sides. Constructing Algebraic Proofs is Higher only. A common slip is setting up consecutive numbers wrongly, and that loses every mark after it. You can search for any video by its name or its code, and the codes are on the list. The quickest way is the scholafly.com website, which lists every video in every subject.

Next in the chapter is Expanding a Single Bracket. Hopefully that's next in your feed, but if not, search for ScholaFly M A ten, oh one.

Every other video is on scholafly.com too, easy to search by video code or by keyword. Whatever you're revising, go there and have a look, or, watch the next video.