Question

How do you translate ${{b}^{2}}-3{{c}^{3}}$ into a verbal expression?

Answer 1

Hint: For translating the given mathematical expression into a verbal expression, we need to name each of the symbols present in it. In the given mathematical expression ${{b}^{2}}-3{{c}^{3}}$, we can see different letters, numbers, the exponents over the letters, and a mathematical operator which is subtraction. The letters denote the different numbers which can be constants or variables. Each letter is to be named along with its exponent and also their coefficients, and then we have to connect the two terms using the “minus” word so that the verbal expression of the given expression will be complete.

Complete step-by-step answer:
The mathematical expression given in the above question is
$\Rightarrow {{b}^{2}}-3{{c}^{3}}$
We can see that the above expression contains two terms ${{b}^{2}}$ and $3{{c}^{3}}$ which are connected with each other using the subtraction operator. For translating it into the verbal expression, we need to translate each and every symbol contained in it verbally. In the above expression, there are different letters which are raised to some exponents. The exponent of $b$ is equal to two, while that of $c$ is equal to three. So we can translate the former as b squared and the latter as c cubed. The c cube term has a coefficient of three so that together it will be pronounced as three times the cube of three. Finally, the two terms are subtracted in the above expression so we will connect the verbal expressions of the two with the minus word. Therefore, the verbal expression of the given mathematical expression becomes “b squared minus three times the cube of c”.
Hence, we have translated the given mathematical expression to a verbal expression.

Note:We may think of translating the given expression as “three squared minus three c cubed”. This translation invites confusion because it can be referred to the cube of three times c as well. Therefore, we must check our verbal expression by translating it back to the mathematical expression.