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Pascal's Triangle: Binomial Expansion

Last updated over 5 years ago

13 Nsɛmmisa

2

2

2

2

2

2

3

3

3

3

2

2

5

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1.

Complete the cells of Pascal's Triangle

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2.

Write out the complete term and include your calculations for determining the coefficient for:
5th term in the expansion of (a + b)⁵

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3.

Write out the complete term and include your calculations for determining the coefficient for:
6th term in the expansion of (c + d)⁸

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4.

Write out the complete term and include your calculations for determining the coefficient for:
2nd term in the expansion of (e + f)⁵

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5.

Write out the complete term and include your calculations for determining the coefficient for:
1st term in the expansion of (g + h)⁵

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6.

Write out the complete term and include your calculations for determining the coefficient for:
5th term in the expansion of (j + k)⁹

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7.

Write out the complete term and include your calculations for determining the coefficient for:
3rd term in the expansion of (m + n)⁴

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8.

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(a + b)⁴ =

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9.

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(c + d)⁷ =

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10.

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(e + f)⁵ =

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11.

Expand completely. HINT: Use the completed Pascal's Triangle above to help you.
(g + h)⁶ =

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12.

What is the coefficient of the term a⁵b³ in (a + b)⁸? Include work/explanation for how you arrived at your answer.

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13.

What is the coefficient of the term a⁴b⁶ in (a + b)¹⁰? Include work/explanation for how you arrived at your answer.