Understanding and applying the binomial theorem

Simplify  $\left(x-4\right)^3.$  

•  $x^3+12x^2+48x-64$  

•  $64-48x+12x^2-x^3$  

•  $x^3+12x^2-16x-4$  

•  $x^3-12x^2+48x-64$  

Find the coefficient of  $y^2$  in the expansion of 

 $\left(y-2\right)^5$  

• 80

• -80

• -320

• 320

Multiply the binomial: (x - 2)⁴

• x⁵ - 8x⁴ + 24x³ - 32x² + 32

• -x⁵ + 8x⁴ - 24x³ + 32x² - 32

• x⁵ + 8x⁴ + 24x³ + 32x² + 32

• x⁵ - 4x⁴ + 6x³ - 4x² + 1

• 6

• 5

• 7

• 4

Expand  $\left(x+y^3\right)^4$  

•  $x^4+4x^3y^3+6x^2y^6+4xy^9+y^{12}$  

•  $x^4+x^3y^3+x^2y^6+xy^9+y^{12}$  

•  $6x^4+15x^3y^3+20x^2y^6+15xy^9+6y^{12}$  

•  $x^4+4x^3y^3+4x^2y^6+4xy^9+y^{12}$  

Describe the signs ( + and - ) in the expanded form of (x + 5)⁴ .

• all +
• all -
• alternating ending in -
• alternating ending in +

( -2x - y )³

• 8x³ − 12x²y + 6xy² − y³
• 8x³ + 12x²y + 6xy² + y³
• -8x³ − 12x²y − 6xy² − y³
• -8x³ + 12x²y − 6xy² + y³

Expand (a⁴-4b)³

(a)