Question

Expand the following using the binomial theorem and Pascal’s triangle.

4.(2x – 3y)4
5.In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning.
a^2b^3; a^5b^3; ab^8; b^8; a^4b^4; a^8; ab^7; a^6b^5

Answer 1

@ganeshie8 I think if I do 4 I'll be able to do 5.

Answer 2

for #4, use the fourth row
http://ptri1.tripod.com/ptreal1r.gif

Answer 3

\[\begin{align}

(2x-3y)^4 &= \bbox[3px, border:2px solid black]{?} (2x)^4(-3y)^0 + \bbox[3px, border:2px solid black]{?} (2x)^3(-3y)^1 + \bbox[3px, border:2px solid black]{?} (2x)^2(-3y)^2 \\~\\&+ \bbox[3px, border:2px solid black]{?} (2x)^1(-3y)^3+ \bbox[3px, border:2px solid black]{?} (2x)^0(-3y)^4

\end{align}\]

Answer 4

okay so did it but then I was going to do what we did with the last question but I don't know what to do with the y ?

Answer 5

fill in the little squares with the coefficients from 4th row of pascal triangle

Answer 6

leave y as it is

Answer 7

it is just another variable like x

Answer 8

so the first one would be -48yx^4

Answer 9

careful, (-3y)^0 = 1

Answer 10

anything^0 = 1

Answer 11

so then it would just be 16x^4 ?

Answer 12

\[\begin{align}

(2x-3y)^4 &= \bbox[3px, border:2px solid black]{1} (2x)^4(-3y)^0 + \bbox[3px, border:2px solid black]{4} (2x)^3(-3y)^1 + \bbox[3px, border:2px solid black]{6} (2x)^2(-3y)^2 \\~\\&+ \bbox[3px, border:2px solid black]{4} (2x)^1(-3y)^3+ \bbox[3px, border:2px solid black]{1} (2x)^0(-3y)^4

\end{align}\]

Answer 13

Yes! first term simplifies to 16x^4
good, keep going..

Answer 14

the second one would be -24yx^3 ?

Answer 15

\[\large 4(2x)^3(-3y)^1\]

this one ?

Answer 16

yes, is what I got wrong?

Answer 17

lets see
\[\large 4(2x)^3(-3y)^1\]

first work the parenthesis
\[\large -4(2^3x^3)(3^1y^1)\]

\[\large -4(8x^3)(3y)\]
\[\large -96x^3y\]

Answer 18

so then it would be -216x^2y^2 ?

Answer 19

it would be +216x^2y^2

because (-1)^2 = 1

Answer 20

try remaining terms :)

Answer 21

I don't think what I got for this one is right because I got -216xy^3

Answer 22

thats right!

Answer 23

finish off the last term

Answer 24

oh okay :) the last one is 81y^4

Answer 25

You got it!

Answer 26

yay thank you so much!!

Answer 27

yw :)

Answer 28

for #5,
just pick the terms whose degree adds up to 8

Answer 29

thanks :)

Answer 30

for example
` a^2b^3` cannot be in the expansion because the degree here is 2+3 = 5 which is not equal to 8.