Binomial Theorem and Pascal's Triangle

Day 54: Pascal Triangle and Binomial Expansion

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Multiple Choice

Given the following tile pattern, how many tiles would be in the 5th shape?

• b = 8

• b = 11

• b = 7

• b = 9

Describing Pascal Triangle

Check for Understanding

Multiple Choice

Choose the right Pascal's triangle

Applying Pascal Triangle to Determine Binomial 

Coefficients of Expansion

Check for Understanding

Multiple Choice

What are the coefficients in the row that must be used to expand (a + b)³?

• 1

• 1 1

• 1 2 1

• 1 3 3 1

Multiple Choice

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

• 5

• 6

• 25

• 50

• 3

Expand Binomial Check for Understanding

Multiple Choice

Expand: $$\left(a+b\right)^3$$  

• $$a^3-3a^2b+3ab^2+b^3$$  

• $$a^3+3a^2b+3ab^{ }+b^3$$  

• $$a^3+3a^2+3ab^2+b^3$$  

• $$a^3+3a^2b+3ab^2+b^3$$  

Multiple Choice

(x − y) ³

• x³ − 3x² y + 3xy² − y³

• 16x ⁴ − 32y ³ + 24x ² − 8x + 1

• x³ − 5x² y + 5xy² − y³