MYTUTOR SUBJECT ANSWERS

323 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,...

7 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

297 SUBJECT SPECIALISTS

PremiumChristopher S. A Level Maths tutor, GCSE Maths tutor, A Level Spanish...
£36 /hr

Chris S.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered:Maths, Spanish+ 1 more

Maths
Spanish
Further Mathematics

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

£20 /hr

Alex W.

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hi i'm Alex. I am currently a first year Maths student at Warwick University, and can tutor you in Maths, Further Maths and Physics at both GCSE and A-Level. I have had plenty of teaching experience before so I can hopefully help you ...”

MyTutor guarantee

£20 /hr

Tom B.

Degree: Mechanical Engineering (Masters) - Southampton University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“Hi, I'm Tom - a first year student at the University of Southampton studying Mechanical Engineering :)”

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

At t seconds, the temp. of the water is θ°C. The rate of increase of the temp. of the water at any time t is modelled by the D.E. dθ/dt=λ(120-θ), θ<=100 where λ is a pos. const. Given θ=20 at t=0, solve this D.E. to show that θ=120-100e^(-λt)

Given that y = exp(2x) * (x^2 +1)^(5/2), what is dy/dx when x is 0?

Integrate 4x^3 + 6x^2 +4x + 3

The line AB has equation 3x + 5y = 7, find; a) the gradient of AB b) the x-axis and y-axis intercepts c) sketch the graph

View A Level Maths tutors

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

mtw:mercury1:status:ok