FOIL Shortcut for Multiplying Two Binomials
Example: $(-7\phi^2+3)(-4\phi^2-5)$
Warning: FOIL applies to binomials ONLY.
Squaring Binomials
To square a binomial, square the first term, add double the inner product, then add the square of the second term.
That is, $(x+y)^2=x^2+2xy+y^2$
The Most Basic Example: $(a+b)^2$
A More Complex Example: $(4x^2-3p)^2$
DIRE WARNING:
PLEASE REMEMBER...
Differences of Squares
Basic Example $(x+y)(x-y)=$
Example: Multiply by inspection. $(4\beta-7 z)(4\beta+7 z)$
Order of Operations
Fact: The order of operations applies to polynomials too.
Example: $(3v - w)(3v + w) - (3v - w)^2$