College Algebra & Trigonometry, 2018a

1.1. ALGEBRAIC SIMPLIFICATION 11
ematics, there are several different approaches that may be taken in simplifying
this problem.
If someone prefers to first distribute the coefficient before multiplying the binomials,
then the coefficient must only be distributed to ONE of the binomials, but
not both. For example, in multiplying 3∗2∗5 =30, we can first multiply 2∗5 =10
and then 3 ∗ 10 = 30. Each factor is multiplied only once.
In the example above we can proceed as we did with the previous example:
2(x +3) 2 − 4(3x − 1)(x +2)=2(x 2 +6x +9)− 4(3x 2 +5x − 2)
=2x 2 +12x +18− 12x 2 − 20x +8
= −10x 2 − 8x +26
Or, we can choose to distribute the 4 first:
2(x +3) 2 − 4(3x − 1)(x +2)=2(x 2 +6x +9)− (12x − 4)(x +2)
=2x 2 +12x +18− (12x 2 +20x − 8)
=2x 2 +12x +18− 12x 2 − 20x +8
= −10x 2 − 8x +26
Or, we can distribute the 4 as a negative. If we do this, then the sign in front of
the parentheses will be positive:
2(x +3) 2 − 4(3x − 1)(x +2)=2(x 2 +6x +9)+(−12x +4)(x +2)
=2x 2 +12x +18+(−12x 2 − 20x +8)
= −10x 2 − 8x +26
Distributing the 2 in front of the squared binomial must also be handled carefully
if you choose to do this. If you distribute the 2 before squaring the (x +3), then
the 2 will be squared as well. If you choose to distribute the 2, the (x +3) 2 must
be written out as (x +3)(x +3):