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Mathematics I (Math 1132)

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Durham College, Mathematics
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Mathematics I (Math 1132)

Simplify Expressions Through Factoring

The skills you’ll learn in this lesson will come in handy unexpectedly one day when you’re stuck trying to simplify what appears to be an impossible expression to reduce. Take a look at the three expressions below:

  1. ab+bcbc+bd
  2. 2x25x34x21
  3. x2ax+2bx2ab2x2+ax3a2

At first glance, you might be questioning how do I divide two polynomials when we’ve only learned how to divide polynomials with monomials? Factoring the numerator and denominator separately should always be considered as an option before devising other plans or giving up. By converting polynomials into factors, you open up the opportunity to cancel with similar factors in the other polynomial, as you’ll see below.

Question: Simplify each expression shown above.

ab+bcbc+bd=ba+cbc+dba+cbc+da+cc+d

✔ Technique: Common factor both the numerator and denominator.

 

2x25x34x21=(2x+1)(x−3)2x12x+12x+1(x−3)2x12x+1=x32x1

✔ Technique: The numerator is factored by decomposition; the denominator is a difference of squares.

 

x2ax+2bx2ab2x2+ax3a2=xxa+2bxax2x+3aa2x+3a=x+2bxaxa2x+3a=x+2b(xa)(xa)2x+3a=x+2b2x+3a

✔ Technique: Factor the numerator by grouping; the denominator is factored by decomposition.

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