Karen W.

asked • 10/23/21

Hi, I need help plz and thank you

  1. g(a)=a3-3a

h(a)=3a-1

Find g(h(a))

1 Expert Answer

By:

Raphael K. answered • 10/23/21

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Hi, I need help plz and thank you

g(a)=a3-3a

h(a)=3a-1

Find g(h(a))

Hello Karen,

find h(a) first,

h(a) = 3a - 1

plug h(a) into g

g(h(a)) = (3a - 1)3 - 3(3a - 1)

Simplify

g(h(a)) =

(3a - 1)(3a - 1)(3a - 1) - 3(3a - 1)

(3a - 1)(3a - 1) ....* Foil these

9a2 - 3a- 3a + 1

9a2 - 6a + 1

Multiply (9a2 - 6a + 1) by (3a - 1)

......... 9a2 - 6a + 1

.................. 3a - 1

————————

........ - 9a2 + 6a - 1

27a3 -18a2 + 3a

—————————

27a3 -27a2 + 9a - 1

Now finish...

27a3 -27a2 + 9a - 1 - 3(3a - 1)

27a3 -27a2 + 9a - 1 - 9a + 3

27a3 -27a2 + 2

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Jeff K.

Here's a much quicker way: From above, g(h(a)) = (3a -1)((3a-1)^2 - 3) = (3a - 1) (9a^2 -6a - 2) . . . . multiplying out the 2nd parenthesis = 27a^3 - 27a^2 + 2 Done!
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10/24/21

Karen W.

Thank You!!!
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10/25/21

Raphael K.

I was being courteous. Use pascals triangle and binomial theorem if you want a shortcut. (a-b)^3 = a^3 -3a^2*b+3a*b^2-b^3
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10/27/21

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