Algebra · Algebraic manipulation
Chapter 1 · 3
The idea
Identities and the ≡ sign
An identity is true for every value of its letter; an equation is true only for some. How to tell whether a statement is true for all, some or no values, why one number can disprove an identity but never prove one, how to show an identity by expanding, and how to find unknown constants by matching coefficients or by choosing values of x.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Algebra · Algebraic manipulation
Identities and the ≡ sign
An identity is true for every value of its letter; an equation is true only for some. How to tell whether a statement is true for all, some or no values, why one number can disprove an identity but never prove one, how to show an identity by expanding, and how to find unknown constants by matching coefficients or by choosing values of x.
Why it works
Two ways to the same area
A square lawn has sides metres long. A path m wide runs along two of its sides, so the lawn and the path together make a bigger square.Priya finds the area of the path as the big square take away the lawn: . Tom adds up two strips and the corner: , which is .Keep reading — free
The rest of the explanation, plus 5 worked examples you step through move by move.
Start freeTakes a minute — no card.