Question

How do you translate to an algebraic expression $x$ plus $y$ squared ?

Answer 1

Hint: In this question, we need to provide an algebraic expression for the given verbal expression. Firstly, note that the algebraic expressions do not contain an equal sign. The skill of translating between verbal statements and algebraic expressions requires an understanding of the words that are commonly used to represent the mathematical operations. In the given question, the expression can be interpreted as two different algebraic expressions.

Complete step by step solution:
Given a verbal expression of the form $x$ plus $y$ squared.
We are asked to translate this to an algebraic expression.
Firstly, let us understand what verbal and algebraic expressions are.
A verbal expression is a mathematical statement that is expressed in words. It is also called a word statement or scale expression. It uses words to describe ideas and math symbols to relate the words.
On the other hand, an algebraic expression has numbers, symbols and variables. It is built up from integer constants, variables and the mathematical operations such as addition, subtraction, multiplication and division.
For example, $5{x^2} - 25xy$ is an algebraic expression.
In the given problem, we have found the algebraic expression for $x$ plus $y$ squared.
The expression can be interpreted as two different algebraic expressions.
(a) If we assume that the word `squared’ refers to the term y only.
Now we start replacing the operators with their symbols.
Plus is represented by the symbol $ + $
Any quantity which is squared is shown as raised to the power of 2. Hence $y$ squared is represented as ${y^2}$.
Thus, the algebraic expression is, $x + {y^2}$
(b) If we assume that the word `squared’ refers to the whole preceding expression $x$ plus $y$, then we raise the power by 2 for $x$ plus $y$.
Thus, the algebraic expression is, ${(x + y)^2}$.

Hence, the algebraic expression for $x$ plus $y$ squared is given by $x + {y^2}$ or ${(x + y)^2}$.

Note :
1) Students must be careful in understanding the words correctly. Since it is simple, they should not make any mistakes in writing. We have to work like a detective to figure out what different words mean. Once we know what those words mean, we will be able to write different variable expressions. The primary difference between the verbal and algebraic expression is an equals sign.
2) Generally verbal expression is a mathematical statement that is expressed in words. And an algebraic expression is the one which contains numbers, symbols and variables.