Use the rules for polynomial operations to simplify the following expression. Show all your computations and explain the steps you take to arrive at your answer.

a. (3x-2)(6x+1)

b. 12t(t + m)(t - 3m)

Question

Use the rules for polynomial operations to simplify the following expression. Show all your computations and explain the steps you take to arrive at your answer.

a.   (3x-2)(6x+1)

b.   12t(t + m)(t - 3m)

jim_thompson5910 · Answer

a)


$$(3x-2)(6x+1)$$



$$(3x)(6x)+(3x)(1)+(-2)(6x)+(-2)(1)$$



$$18x^2+3x-12x-2$$



$$18x^2-9x-2$$



So $$(3x-2)(6x+1)=18x^2-9x-2$$



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b)


$$12t(t + m)(t - 3m)$$



$$12t\left((t)(t)+(t)(-3m)+(m)(t)+(m)(-3m)\right)$$



$$12t(t^2-3mt+mt-3m^2)$$



$$12t(t^2)+12t(-2mt)+12t(-3m^2)$$



$$12t^3-24mt^2-36m^2t$$



So $$12t(t + m)(t - 3m)=12t^3-24mt^2-36m^2t$$