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 cb= b (a c)

• Difference of squares: a² – b² = (a + b)(a – b)

• Sum or difference of cubes: a³ + b³ = (a + b)(a² – ab + b²) and a³ – b³ = (a – b)(a² + ab +b²)

Factoring trinomials:

• Greatest common factor: ax² + ax + ac = a(x² + x + c)

• Un-FOIL: abx² + (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)