Shortcuts

This is where I’ll have various shortcuts.

Quickly Foil $(x-b{)}^2$

If you have something like this

$$\begin{array}{r}(x-8{)}^2\\ (x+3{)}^2\end{array}$$

Instead of manually FOILing it out, you can just do this:
First, be sure to keep the b’s sign the same when doubling it, weird I know!

$$\begin{array}{c}\\ x^2+2(b)+b^2\end{array}$$

So the above examples would be

$$\begin{array}{c}\\ x^2+2(-8)+(-8{)}^2\\ \downarrow \\ x^2-16+64\\ \\ x^2+2(3)+(3{)}^2\\ \downarrow \\ x^2+6+9\end{array}$$

Head shortcuts

These are shortcuts that’re quick enough to do in your head!

• If the last two digits are divisible by 4 then the whole thing is divisible by 4! $\frac{294928}{4}=73732$
• If you want to multiply 11 by any number with 2 digits, add the two digits together and put it in between the two digits! $11\cdot 42=462$
  • if it goes over 9 then you just roll it over! $11\cdot 89=979$