Question

How do you translate “x multiplied by itself, then increased by the product of 12 and y” into an algebraic expression.

Answer 1

Hint: The following problem can be solved in 3 steps. In step 1, we multiply the variable x by itself. In step 2, we multiply a variable y with a number 12. In step 3, we add the expressions derived in step 1 and step 2 that is the sum of expressions x multiplied by itself and the product of 12 and y.

Complete step by step solution:
Algebraic expressions in mathematics are made up of variables, constants, and operators.
Every algebraic expression has variables, coefficients, constants, and terms.
Arithmetic operations like addition, subtraction, multiplication, and division can be performed on Algebraic expressions.
The given question can be solved to get an algebraic expression using 3 steps.
Step 1 is given by,
The variable x is multiplied by itself.
Meaning: The multiplication of variable x with itself means squaring the variable x.
Expression will then be,
$\Rightarrow x\times x={{x}^{2}}$
Step 2 is given by,
The product of 12 and y.
Meaning: The multiplication of a number 12 with a variable y.
Expression will then be
$\Rightarrow 12\times y=12y$
Step 3 is given by,
x multiplied by itself, then increased by the product of 12 and y
Meaning: The sum of x multiplied by itself and product of 12 and y.
Simply, the sum of the expressions in step 1 and step 2.
Final Expression will be given by,
$\Rightarrow {{x}^{2}}+12y$
Hence, the phrase “x multiplied by itself, then increased by the product of 12 and y” upon translation gives an algebraic expression ${{x}^{2}}+12y$

Note: It is very important to change the phrases in English to expressions in maths with the meaning being precisely equivalent. The conversion of phrases to expressions must be done sequentially to avoid confusion.