Which phrase represents 3y+9?
The correct answer and explanation is:
The algebraic expression 3y + 9 can be described as “three times a variable y, plus nine.”
To break it down:
- 3y means “three times y.” This implies that whatever the value of the variable y is, you multiply it by 3.
- +9 simply means adding 9 to the result of 3 times y.
When interpreting algebraic expressions, each term represents a mathematical operation involving a number or variable. In this case:
- The 3y term shows multiplication of the variable y by 3.
- The +9 shows that after multiplying y by 3, you add 9.
This type of expression is considered a binomial, because it contains two terms (3y and 9). Binomials are common in algebra and are part of polynomial expressions, where each term involves variables raised to powers and multiplied by coefficients.
If you were to plug in a value for y, you could compute the actual value of the expression. For example, if y equals 2:
- 3y + 9 becomes 3(2) + 9 = 6 + 9 = 15.
Thus, the expression simplifies to a specific value based on the value of y.
Algebraic expressions like 3y + 9 are fundamental in understanding more complex algebraic concepts, such as solving equations, simplifying expressions, and factoring polynomials.