#### Answer

b

#### Work Step by Step

Simplify each expression. Use the order of operations to determine which terms to simplify first.
a) $4(-2-3)\longrightarrow$ resolve subtraction within parentheses
=$4(-5)\longrightarrow$ multiply
=$-20$
b) $4(-2-3)^2-(-2)\longrightarrow$ resolve subtraction within parentheses
=$4(-5)^2+2\longrightarrow$ resolve exponent; -5 is the factor since the exponent is outside the parentheses
=$4(25)+2\longrightarrow$ multiply
=$100+2\longrightarrow$ add
=$102$
c) $4(-2-3)^3+(-2)\longrightarrow$ subtract within parentheses
=$4(-5)^3+(-2)\longrightarrow$ resolve exponent; -5 is the factor since the exponent is outside the parentheses
=$4(-125)+(-2)\longrightarrow$ multiply
=$-500+(-2)\longrightarrow$ add
=$-502$
d) $\frac{4}{-2}-(-2)(3)\longrightarrow$ divide the fraction
=$-2-(-2)(3)\longrightarrow$ multiply
=$-2-(-6)\longrightarrow$ change subtraction to addition by reversing the sign of the following addend
=$-2+6\longrightarrow$ add
=$4$
At 102, b has the greatest value of the 4 expressions.