Question

How do you translate “ $3$ less than the square of a number $p$ ” as an algebraic expression?

Answer 1

Hint: As we know that algebraic expression is an expression that consists of variables and constants together with algebraic operational signs such that addition, subtraction, exponentiation with the natural exponent and division. Any number more than $(x)$ means that the given number is being added from that number. This type of question is considered a word problem in mathematics.

Complete step by step solution:
Here we are given that we have a number $3$ and we also have another with exponent i.e. $p^2$ (square of a number $p$ ).
Now we put them in the equation as per the statement, less ” means that it is $-3$ less than whatever we are comparing to and a square of $x$ indicates $p^2$ . The equation so formed is $p^2-3$ .
Hence the algebraic expression is $p^2-3$ .
So, the correct answer is “ $p^2-3$ ”.

Note: We should keep in mind that for problems like this, it is good to break up the information and visualize how it fits in together. There is also an alternative way to interpret the question as an inequality. We are given that we have a square of $p$ , it does not mean that $3$ more than $p$ but it is when a variable is in square form. This is a word problem where significant background information on the problem is presented in ordinary language rather than in mathematical notations.