The Binomial Theorem

Pascal's Triangle

100

1 4 6 4 1

What are the binomial coefficients of (a+b)⁴

200

1

What is the number that starts and finishes every row?

300

Get the sum of the two nearest numbers above it.

How do you get the numbers of Pascal's Triangle?

400

1 7 21 35 35 21 7 1

What is (a+b)⁷

500

Coefficients of (a+b)¹¹

What is 1 11 55 165 330 462 462 330 165 55 11 1?

Find the Term

100

The x² term of (x+3)⁴

What is 54x²

200

The x⁶ term of (2x+1)⁸

What is 1792x²

300

The x⁷ term of (3x – 2)¹⁰

What is –2,099,520x⁷

400

The tenth term of (x + 3)¹²

What is 4,330,260x³

500

The sixth term of (2x - 3y)¹¹

What is -7,185,024 x⁶ y⁵

Expand

100

(a+b)³

What is a³+3a²b+3ab²+b³

200

Expand (a-b)³

What is a³-3a²b+3ab²-b³

300

(a+b)⁸

What is a⁸+8a⁷b+28a⁶b²+56a⁵b³+70a⁴b⁴+ 56a³b⁵+28a²b⁶+8ab⁷+b⁸

400

(x − 1)⁶

What is x⁶−6x⁵+15x⁴−20x³+15x²−6x+1

500

Expand the first four terms of (2x – 5y)⁷

What is 128x⁷–2240x⁶y+16,800x⁵y²–70,000x⁴y³

nCr

100

7 C 2

What is 21

200

7 C 3

What is 35

300

16 C ? =11,440

What is 16 C 9

400

56,000,000 C 0

What is 1

500

nC1

n choose 1

n

Express in (a+b)^n form

100

x²+2xy+y²

What is (x+y)²

200

a⁵+5a⁴b+10a³b2+10a²b³+5ab⁴+b⁵

What is (a+b)⁵

300

1-5x+10x²-10x³+5x⁴-x⁵

What is (1-x)⁵

400

4x²+40xy+100y²

What is (2x+10y)²

500

x⁶-30x⁵y+375x⁴y²-2500x³y³+9375x²y⁴-18,750xy⁵+15,625y⁶

What is (x-5y)⁶