Powers of Binomials

Day 56: Expanding Binomial of High Exponents

Do Now

Multiple Choice

Select the coefficients of the 5th Row in Pascal's Triangle

• 1;3;3;1

• 1;4;6;4;1

• 1;5;10;10;5;1

• 1;6;15;20;15;6;1

Combinatorics

Multiple Choice

Evaluate

• A

• B

• C

• D

Expanding Binomial of High Exponents

Multiple Choice

$$The\ term\ independent\ of\ x\ in\ the\ \exp ansion\ of\ \left(x^3+\frac{3}{x^2}\right)^{15}\ is$$  

• $$15_{C_9}\left(3\right)^9$$  

• $$15_{C_6}\left(3\right)^6$$  

• $$15_{C_9}\left(3\right)^4$$  

• $$15_{C_9}\left(3\right)^7$$  

Multiple Choice

$$Fourth\ of\ the\ \exp ansion\ \left(\frac{x}{2}+y\right)^7\ is$$  

• $$\frac{25x^3y^4}{16}$$  

• $$\frac{35x^4y^3}{16}$$  

• $$\frac{70x^4y^3}{16}$$  

• $$\frac{35x^4y^3}{32}$$  

Multiple Choice

Expand the expression using the Binomial Theorem.

(2x+5)⁴

• 2x⁴ + 40x³ + 300x² + 1000x +625

• 16x⁴ + 160x³ +600x² +1000x + 625

• 16x⁴ + 1000x³ + 600x² + 160x +625