Answer :
To express each statement in algebraic language and determine the type of algebraic expressions they are:
a. The cube of any number:
Algebraic expression: \( x^3 \)
Type of expression: Polynomial (specifically a monomial)
b. Twice the sum of two numbers:
Algebraic expression: \( 2(x + y) \)
Type of expression: Polynomial (specifically a binomial)
c. The product of two consecutive numbers:
Algebraic expression: \( x(x+1) \)
Type of expression: Polynomial (specifically a binomial)
d. One third of any number:
Algebraic expression: \( \frac{x}{3} \)
Type of expression: Rational expression
e. One twelfth of any number:
Algebraic expression: \( \frac{x}{12} \)
Type of expression: Rational expression
f. The product of one number and the cube of another:
Algebraic expression: \( x \cdot y^3 \)
Type of expression: Polynomial (specifically a monomial)
These algebraic expressions represent different types of algebraic expressions based on the operations involved (addition, multiplication, division) and the power of variables used. Each expression can be simplified or evaluated further based on the context of the problem or equation in which they are used.
