Factoring difference of squares in two variables
A^2-B^2=(A+B)(A-B)
Example:
9y^2-4z^2
A=3y and B=2z
Answer: (3y+2z)(3y-2z)
Factoring a polynomial involving a GCF and a difference of squares: Multivariate
Factor out GCF or variables and use difference of squares formula A^2-B^2=(A+B)(A-B)
Factoring the sum of two cubes
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
Factoring the difference of two cubes
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Finding roots of quadratic equation with leading coefficient greater than 1
Make the equation equal to 0, factor on left-hand side, solve for variable
Product of expressions equal to zero
A*B=0, if and only if A=0 and B=0
Solving a quadratic equation needing simplification
Rewrite the equation with 0 on one side, use FOIL, combine like terms, factor left side, make variables equal to zero
Solving a word problem using a quadratic equation with rational roots: L and W of rectangle
A=LW
Substitute in part one of word problem
ex: if L=2W- 3 than A= (2W-3)*W
Writing a quadratic equation given the roots and leading coefficient
P=roots
P(#)=0
ex: roots are 3 and 5 so P(3)=0 and P(5)=0 so (x-5) and (x-3)
Multiply roots by lead coefficient- ex: leading coefficient=1
1*(x-5)(x-3)=x^2-8x+15