Homework Help

Use special products to expand the following and simplify: 3a^n(a^n+1 - 2)^2Show...

user profile pic

spock1 | Student, Undergraduate | Honors

Posted July 27, 2011 at 11:03 PM via web

dislike 0 like

Use special products to expand the following and simplify:

3a^n(a^n+1 - 2)^2

Show complete solution to explain the answer.

1 Answer | Add Yours

user profile pic

giorgiana1976 | College Teacher | Valedictorian

Posted July 27, 2011 at 11:14 PM (Answer #1)

dislike 0 like

The factor (a^(n+1) - 2)^2 is the square of a difference and we'll develop the binomial using the formula:

(x-y)^2 = x^2 - 2xy + y^2

Comparing, we'll get:

[a^(n+1) - 2]^2 = a^2(n+1) - 4a^(n+1) + 4

Now, we'll multiply the expansion above by 3a^n:

3a^n*[a^2(n+1) - 4a^(n+1) + 4] = 3a^[n+2(n+1)] - 12a^(n+n+1) + 12a^n

3a^n*[a^2(n+1) - 4a^(n+1) + 4] = 3a^(3n+2) - 12a^(2n+1) + 12a^n

Using special products, we'll get the result 3a^(3n+2) - 12a^(2n+1) + 12a^n.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes