Coefficient of x 2 x^2

Algebra Level 2

What is the coefficient of x 2 x^2 in the expansion of ( 1 + 2 x ) 4 ( 1 − x ) 8 ? (1+2x)^{4}(1-x)^{8}?

-18 -16 -14 -12

Ajay Dutta by Ajay Dutta , 24, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Bhavesh Bhagde
Mar 17, 2014

64-24-28=12

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Jonty Som
Feb 23, 2014

(1+x)^4 (1-x)^8. Expanding with the help of binomial theorem we get (1+4c1.2x+4c2.4x^2+4c3.8x^3+16x^4) (1-8c1.x+8c2.x^2-8c3.x^3+8c4.x^4-8c5.x^5+8c6.x^6-8c7.x^7+x^8). Now here is the trick you multiply and add only those terms which contains only the term x^2.

(1. 8c2.x^2) - (4c1.2x.8c1.x)+ (1.4c2.4x^2) = (28x^2)-(64x^2)+(24x^2) = -12x^2 . So the answer is -12. good luck

0 Helpful 0 Interesting 0 Brilliant 0 Confused

good

Alina Seemab - 7 years, 3 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...