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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: a2b2 = (a + b)(ab)

  • Sum or difference of cubes: a3 + b3 = (a + b)(a2ab + b2) and a3b3 = (ab)(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)

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