- (a+b)² = a²+2ab+b²
- (a-b)² = a²-2ab+b²
- x²+y² is NOT equals to (x+y)²
- x²+y² is equal to (x+y)²-2xy
As for today, we learnt that:
- 201² -402+1 = (201)² -2(201)(1)+(1)²
Note: Before you start doing anything, you need to look out for the relationship between each numbers, and make sure it follows exactly as the quadratic expressions that you learn by heart. In this case, 402 is twice of 201. Since you need to make it exactly the same, there has to be a squared for the 1. Hence, you can square the 1 as the result is still the same.
- 823² -177² = (800-23)² -(800-3)² Do not do this method.
Instead, do this method:
823² -177² = (800-+177)(800-177)
because it is easier to solve. The first method is not encouraged to do as it will take up a very long time to solve.
- All the above sums are called factorisation.
- In factorisation, there are four different methods (but we only learnt two of them today) — By common factors and perfect square.
An example for the common factors method is:
b²-3bc = b(b-3c)
Note: You are actually taking out the HIGHEST common factors, which means ALL the factors must have the same common factors. NOT only one or two of the factors.