Which of the following expressions is equivalent to b x b? A. 2b B.) b^2 C.)2^b D.)2b^2
The Correct Answer and Explanation is :
The correct answer is B) b².
Explanation:
In mathematics, the expression ( b \times b ) is simply the multiplication of the number or variable ( b ) by itself. This is an example of exponentiation, where the base is ( b ) and the exponent (or power) is 2.
When we multiply ( b ) by itself, it is the same as writing ( b^2 ), which is read as “b squared.” This is a standard notation in algebra where:
[
b \times b = b^2
]
Now, let’s break down why the other options are not equivalent to ( b \times b ):
- A) 2b: This is the expression where ( 2 ) is multiplied by ( b ), which is not the same as multiplying ( b ) by itself. Therefore, it is incorrect.
- C) 2^b: This means 2 raised to the power of ( b ), which is a different mathematical operation. It suggests that the base is 2, not ( b ), and the exponent is ( b ). This is not the same as ( b \times b ), so it is also incorrect.
- D) 2b²: This expression means 2 multiplied by ( b^2 ), which is not the same as ( b \times b ). The presence of the coefficient 2 in front of ( b^2 ) changes the value, so it is also not equivalent.
Why ( b^2 )?
The operation ( b \times b ) is the definition of squaring a number or variable. When we square a number, we are multiplying it by itself, and the notation for this operation is ( b^2 ). Exponentiation is a shorthand for repeated multiplication, and ( b^2 ) represents the result of multiplying ( b ) by itself.
Thus, ( b \times b = b^2 ) is the simplest and most accurate representation of the expression.