Pascal's triangle

What is the binomial expansion of (x + 1)⁸ ?

• x⁸ + 1

• x⁸ + 8x⁷ + 16x⁶ + 24x⁵ + 32x⁴ + 24x³ + 16x² + 8x + 1

• x⁸ + 7x⁷ + 21x⁶ + 35x⁵ + 35x⁴ + 21x³ + 7x² + 1

• x⁸ + 8x⁷ + 28x⁶ + 56x⁵ + 70x⁴ + 56x³ + 28x² + 8x + 1

• x⁸ + 8x⁷ + 28x⁶ + 70x⁴ + 56x³ + 28x² + 8x + 1

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If the top row of Pascal's Triangle is row 0, then what is the sum of the numbers in the eighth row?

• 255

• 256

• 257

• 260

• 264

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The diagram shows how the numbers of the Fibonacci sequence can be obtained from the numbers in Pascal's Triangle.

Following the same pattern, which numbers of Pascal's triangle can be added together to give the next number of the Fibonacci sequence?

• 34 = 1 + 8 + 15 + 9 + 1

• 34 = 1 + 7 + 10 + 10 + 5 + 1

• 34 = 1 + 2 + 15 + 15 + 1

• 34 = 1 + 7 + 15 + 10 + 1

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What is row 17, term 5 in Pascal's triangle?

• 2,380

• 4,368

• 6,188

• 12,376

• 5,284

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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

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What is the Binomial expansion of (a − b)⁷ ?

• a⁷ − b⁷

• a⁷ + 7a⁶b + 21a⁵b² + 35a⁴b³ + 35a³b⁴ + 21a²b⁵ + 7ab⁶ + b⁷

• a⁷ + 7a⁶b − 21a⁵b² + 35a⁴b³ − 35a³b⁴ + 21a²b⁵ − 7ab⁶ + b⁷

• a⁷ − 7a⁶b + 21a⁵b² − 35a⁴b³ + 35a³b⁴ − 21a²b⁵ + 7ab⁶ − b⁷

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The Pascal's Triangle is named after

• Mary Pascal

• Blain Pascal

• Blaise Pascal

• Joshua Pascal

• Pascal Pascal

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Which row of the Pascal's Triangle is the number 6 first found in?

• 3rd

• 4th

• 5th

• 6th

• 2nd

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

• 5

• 6

• 25

• 50

• 3

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How is the binomial expansion of (1+b)ⁿ different from (1-b)ⁿ ?

• They have a different number of terms.

• Their coefficients have alternate + and - signs.

• They have different degrees.

• There is no difference

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