MYTUTOR SUBJECT ANSWERS

123 views

Simple binomial: (1+0.5x)^4

Expand (1+0.5x), simplifying the coefficients. 

1. Draw Pascal's triangle to find the coefficients

            1

     1     2     1

   1    3     3     1 

1    4    6     4     1 

As you can see, each row starts and ends with 1. The numbers in between are worked out by adding the two numbers on top. 

For this question, we will be using the 1 4 6 4 1 row because the expression is raised to the power of 4. This expansion will have 5 expressions. 

2.  For each term, both 1 and 0.5 are raised to powers 0 to 4, where the sum of the powers always adds up to 4. In addition, the power of x is increased from 0 to 4 as the term progress. 

(1+0.5x)

1(1)4(0.5)0x04(1)3(0.5)1 x1 + 6(1)2(0.5)x24(1)1(0.5)3 x3+ 1(1)0(0.5)x4

First, we raising 1 to the power of 4, therefore 0.5 is raised to the power of 0. For the next term, the power of 1 decreased by 1 and the power of 0.5 increases by 1, so that the sum of the terms still equates to 4. This is done until we get 5 terms in total. 

3.  The expression can be simplified as followed: 

= 1 + 4(1/2)x + 6(1/4)x+  4(1/8)x3 + (1/16)x

= 1 + 2x + 3/2x+ 1/2x+ 1/16x4

Srikka S. 11 Plus Maths tutor, GCSE Maths tutor, A Level Maths tutor,...

3 months ago

Answered by Srikka, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

182 SUBJECT SPECIALISTS

£20 /hr

Calum C.

Degree: Economics (Bachelors) - Durham University

Subjects offered: Maths, Latin+ 1 more

Maths
Latin
Economics

“Hello there! I am Calum a current undergraduate Economics studnet at Durham university in my 1st year. If you would like to learn economics, maths or even latin from someone so eccentric and enthusiastic you will not be bored, ask me!”

MyTutor guarantee

£20 /hr

Laura P.

Degree: Natural Sciences (Masters) - Lancaster University

Subjects offered: Maths

Maths

“Hi! I'm Laura, a Natural Scientist at Lancadter University, where I study Maths and Phyiscs. I have such a passion for these subjects that I hope my tutorials will be both engaging and interactive, because the best way of learning is ...”

MyTutor guarantee

£20 /hr

Jennifer L.

Degree: Mathematics with Finance (Bachelors) - Exeter University

Subjects offered: Maths, Chemistry

Maths
Chemistry

“Top tutor from Exeter University studying Maths with Finance, ready to help you improve your grades in Maths and Chemistry!”

MyTutor guarantee

About the author

£20 /hr

Srikka S.

Degree: Electrical & Electronics Engineering (Masters) - Bristol University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
French
-Personal Statements-

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other A Level Maths questions

If (m+8)(x^2)+m=7-8x has two real roots show that (m+9)(m-8)<0 where m is an arbitrary constant

What modules have you done before?

How to transform graphs of functions?

How do you integrate by parts?

View A Level Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok