Question

Define the binary operation $ by a$b = ab 2a – 3b. Find x$(2$x).

A) 4x
B) 6x
C) 8x
D) 10x

Answer 1

To solve x$(2$x), we apply the operation rule twice. First, we calculate 2$x, then use the result to find x$(2$x), which simplifies to 4x (Option A).

Step-by-step explanation:

The binary operation $ is defined by the expression a$b = ab + 2a - 3b. To find x$(2$x), we apply the given operation rule. First, find the result of 2$x: 2$x = 2x + 2(2) - 3x. This simplifies to 4 + x. Now, apply the operation again to find x$(2$x): x$(4 + x) = x(4 + x) + 2x - 3(4 + x).

To find x$(2$x), we need to substitute the given expression into the defined binary operation. Let's start by replacing the variables:

x$(2$x) = x(2x)2x - 3(2x)

Simplifying further:

x(2x)2x - 3(2x) = 2x^2(2x) - 3(2x)

Applying the exponent rule, (xa)b = xa.b:

2x^2(2x) - 3(2x) = 2(x^2).(2x) - 3(2x)

Combining like terms:

2(x^2).(2x) - 3(2x) = 4x^3 - 6x

Therefore, x$(2$x) = 4x^3 - 6x.

Therefore, the direct answer is 4x (Option A).