# Solve Trigonometry Equations by Factoring

The same type of factoring that algebra uses to solve equations is a great help in solving trigonometry equations. The only trick with the trig equations is to recognize that instead of just *x**'*s, *y**'*s, or other single-letter variables, trig variables such as sin *x* or sec *y* exist.

Here’s a list of the basic factoring patterns so that you know which factoring techniques to apply.

**Factoring binomials:**

Greatest common factor:

*ab**c**b*=*b*(*a**c*)Difference of squares:

*a*^{2}–*b*^{2}= (*a*+*b*)(*a*–*b*)Sum or difference of cubes:

*a*^{3}+*b*^{3}= (*a*+*b*)(*a*^{2}–*ab*+*b*) and^{2}*a*^{3}–*b*^{3}= (*a*–*b*)(*a*^{2}+*ab*+*b*)^{2}

**Factoring trinomials:**

Greatest common factor:

*ax*^{2}+*ax*+*ac*=*a*(*x*^{2}+*x*+*c*)Un-FOIL:

*abx*^{2}+ (*ad*+*bc*)*x*+*cd*= (*ax*+*c*)(*bx*+*d*)

**Factoring by grouping:**

*abxy*+*adx*+*bcy*+*cd**=**ax**by*+*d*) +*c*(*by*+*d*)*=*(*ax*+*c*)(*by*+*d*)