Binomial Theorem and Pascal's Triangle

Binomial Expansion L1

By Henry Phan

​Pascal's Triangle

​•Pascal’s triangle help to determine all coefficients of a binomial expansion. Where a, b ∈ R, and exponent n ∈ N

​Start with number “1” at the top, then continue placing numbers below by the sum of two consecutive numbers on the same row.

​Pascal's Triangle

​•Pascal’s triangle help to determine all coefficients of a binomial expansion. Where a, b ∈ R, and exponent n ∈ N

​Start with number “1” at the top, then continue placing numbers below by the sum of two consecutive numbers on the same row.

​Pascal's Triangle

​•Pascal’s triangle help to determine all coefficients of a binomial expansion. Where a, b ∈ R, and exponent n ∈ N

​Start with number “1” at the top, then continue placing numbers below by the sum of two consecutive numbers on the same row.

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Expand (x - 2)³

Expand (x - 2)³

1x³(-2)⁰ + 3x²(-2)¹ + 3x¹(-2)² + 1x⁰(-2)³

1x³ + 3x²(-2) + 3x¹(4) + 1x⁰(-8)

x³ - 6x² + 12x - 8

Math Response

Expand each expression:

$$\left(x+2\right)^3$$

Type answer here

Correct Answer: x^3+6x^2+12x+8

Deg^°

Rad

Math Response

Expand each expression:

$$\left(x-4\right)^5$$

Type answer here

Correct Answer: x^5-20x^4+160x^3-640x^2+128x-1024

Deg^°

Rad

Math Response

Expand each expression:

$$\left(3x+1\right)^4$$

Type answer here

Correct Answer: 81x^4+108x^3+54x^2+12x+1

Deg^°

Rad

Math Response

Expand each expression:

$$\left(3a-b\right)^3$$

Type answer here

Correct Answer: 27a^3-27a^2b+9ab^2-b^3

Deg^°

Rad

Multiple Choice

Expand

$$\left(3n+1\right)^4$$  

• $$81n^4+108n^3+54n^2+12n+1$$  

• $$81n^4-27n^3+9n^2-3n+1$$  

• $$12n^4+9n^3+6n^2+3n+1$$  

• $$81n^4+27n^3+9n^2+3n+1$$