Question

Find the third term in the expansion of (a + 3b)^7.
a. 756a^4b^3
b. 42a^3b^4
c. 189a^5b^2
d. 210a^3b^4


Find the fourth term in the expansion of (4x + 3y)7.

a. 181,440x^3y^4
b. 181,440x^4y^3
c. 241,920x^4y^3
d. 241,920x^3y^4

Answer 1

To begin, you first need to understand the pattern to binomial expansion. In binomial expansion there are three things to take into account: the two values which make the term (in your case it will be a and 3b from the expression (a+3b)^7 for the first problem and 4x and 3y for the second problem), the coefficient in front of the term, and to which power each part of the term will be taken to.

This link shows the pattern for which expansion occurs (in your case, you'll want to look at the bottom row to see how a binomial to the power of 7 is expanded): http://wpcontent.answcdn.com/math/0/5/9/05912cb66ba1a0cc47688071d5cdae8a.png

to understand where the coefficients come from you'll need to reference Pascal's Triangle (specifically the 8th row): http://www.mathsisfun.com/images/pascals-triangle-4.gif

In the link, x and y are used as placeholders for the two values that you have (a and 3b). The third term will be 21*(a)^5(3b)^2 (which equates to answer c) and the fourth term will be 35(4x)^4(3y)^3 (which equates to answer c).

Btw sorry if this answer is long and complicated. Hopefully it makes sense :)

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Answer 2

thank you! your links and explanation helped a lot! thanks again!