Question 1116458
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I'll get you started by explaining how to get a few terms of the first example; then you can continue the process to finish that one and do the second one.<br>
{{{(y-3z)^5}}}<br>
Think of this as 5 factors of (y-3z) multiplied together.  The final expanded form consists of all the "partial products" formed by choosing one of the two terms from each of the 5 factors.  For example, one partial product, obtained by choosing the "y" term from the first 2 of the 5 factors and the "-3z" term from the last 3 factors, is {{{(y)^2*(-3z)^3 = -27y^2z^3}}}.<br>
I will show you how to get the first three terms in the expansion of this first example....<br>
(1) If you choose the "y" term from all 5 of the factors, the partial product is {{{y^5}}}.  And there is only one way to choose the "y" term from all 5 of the factors; so the first term in the expansion is {{{y^5}}}.<br>
(2) If you choose the "y" term from 4 of the 5 factors and the "-3y" term from the other, then the partial product is {{{(y)^4*(-3z)^1 = -3y^4z}}}.  The number of different ways of choosing the "y" term in 4 of the 5 factors is "5 choose 4", or {{{C(5,4) = 5}}}.  So the second complete term in the expansion is {{{5*(-3y^4z) = -15y^4z}}}.<br>
(3) Without all the explanation, the next complete term in the expansion will be {{{C(5,3)*(y)^3*(-3z)^2 = (10)(y^3)(9z^2) = 90y^3z^2}}}.<br>
Now see if you can finish your two problems.