For all real numbers a and b, the custom operation \star is defined by a \star b = (a + b)… — GMAT

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

Substituting

a = 4

and

b = 2

into the definition

(a + b)^2 - 3b

gives

(4 + 2)^2 - 3(2) = 6^2 - 6 = 36 - 6 = 30

Identify the values assigned to the custom operator variables

a = 4

and

b = 2

The expression

4 \star 2

corresponds to evaluating

a \star b

where

a

is the first operand and

b

is the second operand.

Substitute

a = 4

and

b = 2

into the operator definition

(a + b)^2 - 3b

(4 + 2)^2 - 3(2)

Direct substitution into the given algebraic definition.

Perform the operations in parentheses and exponentiation

6^2 - 6 = 36 - 6

First add inside the parentheses (

4 + 2 = 6

), then square the sum (

6^2 = 36

), and multiply

3 \times 2 = 6

Subtract to find the final value

Subtracting

6

from

36

yields

30

Custom Operator Evaluation

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