Write the expression. A number b squared
The Correct Answer and Explanation is :
To express “a number ( b ) squared,” we use the mathematical notation:
[
b^2
]
Explanation
In mathematics, squaring a number means multiplying the number by itself. This operation is a fundamental concept in algebra and is denoted by raising the number to the power of 2. The notation ( b^2 ) reads as “b squared” or “b to the power of two.”
For example, if we have ( b = 3 ), then squaring it would be:
[
b^2 = 3^2 = 3 \times 3 = 9
]
Properties of Squaring a Number
- Positive and Negative Numbers: Squaring a number always results in a non-negative value. This is because multiplying two positive numbers yields a positive product, and multiplying two negative numbers also results in a positive product. For instance:
- ( (-4)^2 = (-4) \times (-4) = 16 )
- ( (5)^2 = 5 \times 5 = 25 )
- Zero: The square of zero is zero:
[
0^2 = 0 \times 0 = 0
] - Area Representation: The concept of squaring can also be visually understood in geometry. If you consider a square shape with sides of length ( b ), the area of the square is given by ( b^2 ). This relationship between squaring and area is crucial in various mathematical applications.
- Algebraic Expansions: Squaring a binomial, such as ( (b + c)^2 ), can be expanded using the formula:
[
(b + c)^2 = b^2 + 2bc + c^2
]
This illustrates how squaring is connected to polynomial expressions.
Conclusion
In summary, the expression ( b^2 ) represents the square of the number ( b ), which encapsulates the idea of multiplication of ( b ) by itself. Squaring is an essential operation with wide-ranging applications across different areas of mathematics, from basic arithmetic to complex algebraic calculations.