Binomial Theorem & Pascal’s triangle

Category 1

100

condense

x³+3x²y+3xy²+y³

(x+y)³

200

What is the coefficient order for the power of 4 of Pascal’s triangle?

1,4,6,4,1

300

(a+b)³

a³+3a²b+3ab²+b³

400

Fill in the row  

1,4,?,?,1

6,4

500

Unscramble 

1,126,126,9,36,9,84,84,1,36

1,9,36,84,126,84,36,9,1

Category 2

100

What is missing 

1,3,?,1

3

200

(x+z)⁴

x⁴+4x³z+6x²z²+4xz³+z⁴

300

a^4,-4ab³,b^4,6a²b²,-4a³b

a⁴-4a³b+6a²b²-4ab³+b⁴

400

(2a-b)⁵

32a⁵-80a⁴b+80a³b²-40a²b³+10ab⁴-b⁵

500

a⁵+5a⁴b+?a³b²+10a²b^?+5ab⁴+b⁵

10,3

Category 3

100

(o+n)^3*6-14

o⁴+4no³+6n²o²+4n³o+n⁴

200

3ab²,a³+,+,3a²b,+,b³

a³+3a²b+3ab²+b³

300

Write the coefficient order for the power of 10

1,10,45,120,210,252,210,120,45,10,1

400

condense

x⁸+8x⁷y+28x⁶y²+56x⁵y³+70x⁴y⁴+56x³y⁵+28x²y⁶+8xy⁷+y⁸

(x+y)⁸

500

coefficient order for power of 9

1, 9, 36, ,84, 126, 126, 84, 36,9, 1

Category 4

100

(x+y)^3

x³+3x²y+ 3xy²+y³

200

Coefficient order for the power of 4

1, 4,6,4,1

300

(p+r)(p+r)

p²+2pr+r²

400

1, ?, ?, 20, ?, ?, 1

1, 6, 15, 20, 15,6,1

500

(y+m)(y+m)(y+m)

y³+3y²m+3ym²+m³

Category 5

100

unscramble

7, 1, 1, 21, 7, 35, 21, 35

1,7,21,35,21,7,1

200

unscramble

b⁵, 10a³b², 5a⁴b, 10a²b^5, a⁵, 5ab⁴

a⁵+5a⁴b+10a³b²+10a²b³+5ab⁴+b⁵

500

(a+b)¹³

a¹³+13a¹²b+78a¹¹b²+286a¹⁰b³+715a⁹b⁴+1287a⁸b⁵+1716a⁷b⁶+1716a⁶b⁷+1287a⁵b⁸715a⁴b⁹+286a³b¹⁰+78a²b¹¹+13ab¹²+b¹³