For all real numbers a and b, the custom operation \star is defined by a \star b = a(b + 2… — GRE General Test

For all real numbers $a$ and $b$ , the custom operation $\star$ is defined by $a \star b = a(b + 2) - b$ . What is the value of $4 \star (-3)$ ?

-1

Substituting

a = 4

and

b = -3

into the given operation gives

4((-3) + 2) - (-3) = 4(-1) + 3 = -4 + 3 = -1

. The value of the expression is

-1

Substitute

a = 4

and

b = -3

into the custom operation formula

a \star b = a(b + 2) - b

4 \star (-3) = 4((-3) + 2) - (-3)

The definition specifies replacing variable

a

with

4

and variable

b

with

-3

Evaluate the expression inside the parentheses.

-3 + 2 = -1

, simplifying the expression to

4(-1) - (-3)

Perform operations inside grouping symbols first according to the standard order of operations.

Perform the multiplication and simplify the double negative.

4(-1) = -4

and

-(-3) = +3

, yielding

-4 + 3 = -1

Multiplying positive and negative yields negative, and subtracting a negative number is equivalent to addition.

Evaluating Custom Binary Operations

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