Binomial Expansion Using Combinations

Binomial Expansion

How do I expand binomials using Pascal's Triangle?

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​MGSE9-12.A.APR.5 Know and apply that the Binomial Theorem gives the expansion of binomials in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined using Pascal’s Triangle

How do I expand binomials using Pascal's Triangle?​

​MGSE9-12.A.APR.5 Know and apply that the Binomial Theorem gives the expansion of binomials in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined using Pascal’s Triangle

Pascal's Triangle: A Pattern for Expanding Binomials

Multiple Choice

• 3, 10, 7

• 2, 5, 1

• 3, 10, 21

• 2, 10, 7

• 4, 6, 6

​Expand the binomial with Pascal's Triangle.

How do I expand binomials using Pascal's Triangle?​

​MGSE9-12.A.APR.5 Know and apply that the Binomial Theorem gives the expansion of binomials in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined using Pascal’s Triangle

​1. Find the numbers from the appropriate row of the triangle.

​2. Set up a 3-row table.

​3. Multiply Down

​4. If binomial is subtraction, alternate signs in final answer. If it is addition, all signs are positive.

​Expand the binomial with Pascal's Triangle.

​1. Find the numbers from the appropriate row of the triangle.

​2. Set up a 3-row table.

​3. Multiply Down

​4. If binomial is subtraction, alternate signs in final answer. If it is addition, all signs are positive.

How do I expand binomials using Pascal's Triangle?​

​MGSE9-12.A.APR.5 Know and apply that the Binomial Theorem gives the expansion of binomials in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined using Pascal’s Triangle

Multiple Choice

Expand completely.

$$\left(2n+m\right)^3$$  

• $$32n^3+24n^2m+8nm^2+m^3$$  

• $$8n^3+12n^2m+6nm^2+m^3$$  

• $$8n^3+12n^2m+6nm^2+m^3$$  

• $$40n^3+40n^2m+20nm^2+5m^3$$  

Multiple Choice

Expand completely. $$\left(m-4\right)^4$$  

• $$5m^4-40m^3+160m^2-320m+256$$  

• $$-3m^4-16m^3+96m^2-256m+256$$  

• $$m^4-4m^3+16m^2-64m+256$$  

• $$m^4-16m^3+96m^2-256m+256$$  

Multiple Choice

Expand completely.

$$\left(2x+1\right)^3$$  

• $$8x^3+32x^2+6x+1$$  

• $$40x^3+40x^2+20x+5$$  

• $$8x^3+24x^2+6x+1$$  

• $$8x^3+12x^2+6x+1$$