Binomial Help! (1 Viewer)

[Uzername]

Question: in the following expansion: <a href="http://www.codecogs.com/eqnedit.php?latex=(1@plus;x)^{5}(1@plus;x)^{6}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?(1+x)^{5}+(1+x)^{6}" title="(1+x)^{5}+(1+x)^{6}" /></a>

a) factorise it,
b) find the coefficient of <a href="http://www.codecogs.com/eqnedit.php?latex=x^{3}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?x^{3}" title="x^{3}" /></a>.

the answers are,
a) <a href="http://www.codecogs.com/eqnedit.php?latex=(2@plus;x)(1@plus;x)^{5}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?(2+x)(1+x)^{5}" title="(2+x)(1+x)^{5}" /></a>
b) 30.

My textbook doesn't explain how to get to these answers, so could someone please help out? Thanks!

 

[AAEldar]

For a:

 

[SpiralFlex]

a)


b) On your calculator there is a button called . By definition, the coefficient of in the expansion . So we want the coefficient of in ADDED onto the coefficient of in .

That would be which is .