Y12 Pascals Triangle/Binomial Expansion

Y12 Pascals Triangle/Binomial Expansion

Chapter 4

This is how you create pascals triangle, write it down if you didn't know.

Multiple Choice

Choose the right Pascal's triangle

Multiple Choice

How many rows in The Pascal's triangle?

• 7

• 8

• 100

• Infinite

FUN FACT! The powers of 11 are embedded in Pascals triangle.

Another fun fact

The reason we are interested in Pascals for Chapter 4 is to use it as a quick way to find the coefficients of expanding polynomials.

Please copy this example if you haven't done it before, and the one on the next slide.

Then be prepared to answer some questions.

TIP- the index for both terms always adds up to the power in the question

Still a bit confused?

No problem, watch section 1 and 2 for more explanations and examples.

The video is an hour long and goes into things which are later on in the Chapter. So only watch the first few sections for now.

Poll

Are you going to watch the video

• No, I have done this before and ready to try the questions.

• Yes I just want to look at a few more examples.

Multiple Choice

Which row of Pascal's Triangle would you use to expand (x+y)³?

• 1
• 1  1
• 1  2  1
• 1  3  3  1

Multiple Choice

Select the correct expansion of

(1 + 4x)³

• 1 + 12x + 12x² + 4x³

• 1 + 12x + 48x² + 64x³

• 1 + 3x + 3x² + x³

• 1 + 4x + 16x² + 64x³

Multiple Choice

What is the Binomial expansion of (x + 1)⁵ ?

• x⁵ + 5x⁴ + 10x³ + 10x² + 5x + 1

• x⁵ + 5x⁴ + 15x³ + 15x² + 5x + 1

• x⁵ + 6x⁴ + 15x³ + 15x² + 6x + 1

• x⁵ + 1

Multiple Choice

Find the 2nd term in the expansion of 
(2b + 1)³

• 12b²
• 6b
• 8b³
• 4b²

Multiple Choice

How many terms are the in the expansion of (1+b)⁵

• 5

• 6

• 25

• 50

• 3

Multiple Choice

Expand the expression.
(2x+5)⁴

• 2x⁴ + 40x³ + 300x² + 1000x +625
• 16x⁴ + 160x³ +600x² +1000x + 625
• 16x⁴ + 1000x³ + 600x² + 160x +625

Multiple Choice

Find the 4th term in the expansion of (4x-3)⁵.

• 5760

• -4320x²

• 5760x³

• -4320

Now carry on with the sheet from last lesson

EXTENSION:

A-level textbook exercise on the next slide.

Finding unknown values

Set up an equation, like in the example. Copy this down if you want.

Complete these from Exercise 4A (page 64)

Next lesson...

Please write down these notes for next lesson.

Ask me for the answers once you have finished the questions on the previous slides.