Understanding and applying the binomial theorem

Expand  $\left(4x-y\right)^3$  

•  $64x^3-48x^2y+12xy^2-y^3$  

•  $64x^3-16x^2y+4xy^2-y^3$  

•  $256x^3-96x^2y+16xy^2-y^3$  

•  $320x^3-160x^2y+40xy^2-5y^3$  

Which can be brought together into this: a^n-kb^?

What should the ? be?

 $\left(3x+5\right)^4$  

•  $12x^4+3x^3+15x^2+5x+15$  

•  $81x^4+135x^3+225x^2+375x+625$  

•  $81x^4+540x^3+1350x^2+1500x+625$  

The first three terms of (x + 1)⁸ are ...

• 1 + 8 + 28
• x⁸ + x⁷ + x⁶
• 1 + 8x + 28x²
• x⁸ + 8x⁷ + 28x⁶

• None of these

Which expression represents the sixth term in the binomial expansion of

 $\left(2a-3b\right)^{10}$  

• ₁₀C₅(2a)⁵(-3b)⁵ 

• ₁₀C₅(-2a)⁵(3b)⁵ 

• ₁₀C₆(2a)⁴(-3b)⁶ 

• ₁₀C₆(-2a)⁴(3b)⁶ 

  
  

• ₁₀C₆(2a)⁶(-3b)⁴ 

What is the coefficient of the fifth term in the expansion of

 $\left(3x-3y\right)^7$  ? 
 $?x^3y^4$  

Find the coefficient of y³ in the expansion of (1 - 3y)¹⁴ by using combination

• -9828

• 9828

• 364

• -364

Find the fourth term of the expansion (5+3y)⁵ by using combination

• 2025y⁴

• 750y³

• 75y⁴

• 6750y³