Question

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

3.(2x + 3)^5

Answer 1

@ganeshie8

Answer 2

I've done up to a certain point but I don't know how to go on.

Answer 3

pick the 5th row for coefficients
http://ptri1.tripod.com/ptreal1r.gif

Answer 4

I know but I thought the 2 in 2x was the coefficient which is why I'm confused.

Answer 5

\[\begin{align}

(2x+3)^5 &= \square (2x)^5(3)^0 + \square (2x)^4(3)^1 +\square (2x)^3(3)^2 +\square (2x)^2(3)^3 \\~\\&+\square (2x)^1(3)^4 +\square (2x)^0(3)^5

\end{align}\]

Answer 6

fill in the little squares with the coefficients from 5th row of pascal triangle

Answer 7

okay and then just multiply the numbers by 2x?

Answer 8

kindof : \[\begin{align}

(2x+3)^5 &= \bbox[3px, border:2px solid black]{1} (2x)^5(3)^0 + \bbox[3px, border:2px solid black]{5} (2x)^4(3)^1 + \bbox[3px, border:2px solid black]{10} (2x)^3(3)^2 + \bbox[3px, border:2px solid black]{10} (2x)^2(3)^3 \\~\\&+ \bbox[3px, border:2px solid black]{5} (2x)^1(3)^4 + \bbox[3px, border:2px solid black]{1} (2x)^0(3)^5

\end{align}\]

Answer 9

simplify each term

Answer 10

whats the valie of (2x)^5 ?

Answer 11

uh...32x ?

Answer 12

the exponent applies to both the factors

(2x)^5 = 2^5*x^5 = 32x^5

Answer 13

so just keep doing that with all of them...

Answer 14

Yep

Answer 15

so how would I do it for 10x^4 because that's 10,000x^4 ?

Answer 16

are you refering to below term ?\[\large 5(2x)^4(3)^1\]

Answer 17

yes :)

Answer 18

first work the parenthesis :
\[\large 5(2^4x^4)(3^1)\]

Answer 19

simplifying gives
\[\large 5(16x^4)(3)\]

furthher simplifying you get
\[\large 240x^4\]

Answer 20

go ahead, try simplifying remaining terms. im sure you will be able to work them :)

Answer 21

ohhhhh I get it now thanks

Answer 22

nice, so whats the final answer ?

Answer 23

\[32x ^{5} + 240x ^{4} + 720x ^{3} + 1080x ^{2} + 810x + 243\]

Answer 24

Perfect!
you may double check your answer wid wolfram
http://www.wolframalpha.com/input/?i=expand+%282x+%2B+3%29%5E5

Answer 25

thank you so much!! can you help with one more? or just the first part because I think its the same process but I want to make sure I get it right?

Answer 26

wil try, please open a new q :)