MYTUTOR SUBJECT ANSWERS

271 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,...

6 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

256 SUBJECT SPECIALISTS

£20 /hr

Henry T.

Degree: Economics (Bachelors) - Leeds University

Subjects offered: Maths, Economics

Maths
Economics

“About me: I am a 20 year old third year economics student, currently achieving a first class degree at the Univesity of Leeds. Economics and Maths are two subjects that genuinely excite me. My degree allows me to study economics but al...”

MyTutor guarantee

£20 /hr

Yusuf C.

Degree: Mathematics (Bachelors) - Liverpool University

Subjects offered: Maths

Maths

“I am an enthusiastic and passionate maths tutor who is dedicated to help you improve your grades”

MyTutor guarantee

£20 /hr

Matthew S.

Degree: Economics (Bachelors) - Exeter University

Subjects offered: Maths, History+ 2 more

Maths
History
Extended Project Qualification
Economics

“Who am I? I am a 3rd Year Economics Student at the University of Exeter. Economics has always been at the top of my interests meaning that I have real passion for all things economics and math based which I will aim to instill into my...”

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

Differentiation basics: What is it?

What is trigonometry? How do I remember sine, cosine and tangent?

find the integral for xe^10x

What is Differentiation?

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