1 less than the square of a number.
The correct answer and explanation is:
The expression “1 less than the square of a number” can be written mathematically as: x2−1x^2 – 1
Where xx is the variable representing the number. To understand this expression, let’s break it down:
- Square of a number: This means multiplying the number by itself. For instance, the square of 3 is 32=93^2 = 9.
- 1 less than the square: Once you find the square of the number, you subtract 1 from it. For example, if the number is 3, the square is 9, and 1 less than 9 is 8.
Example
Let’s take an example to understand how the expression works:
If the number is 4, the square of 4 is: 42=164^2 = 16
Then, 1 less than the square is: 16−1=1516 – 1 = 15
So, for x=4x = 4, the result of the expression x2−1x^2 – 1 is 15.
Generalization
The expression x2−1x^2 – 1 is also known as a difference of squares. This is because: x2−1=(x−1)(x+1)x^2 – 1 = (x – 1)(x + 1)
This identity shows that you can factor the expression as the product of two binomials. This can be useful when simplifying algebraic expressions or solving equations.
Conclusion
In summary, “1 less than the square of a number” refers to the mathematical operation where you take the square of a number and subtract 1 from it. The result is expressed as x2−1x^2 – 1, and for any given number xx, you can calculate it by squaring the number and then subtracting 1.