Which statement is correct when solving the expression $5 y^2-3 y^2 $?
A. Add the coefficients $(5+3)$.
B. Add the exponents $(2+2)$.
C. Subtract the exponents (2-2).
D. Subtract the coefficients (5-3).
Answer (1)
The problem requires simplifying the expression 5 y 2 − 3 y 2 by combining like terms.
Identify that both terms have the same variable y raised to the power of 2.
Subtract the coefficients: 5 − 3 = 2 .
Keep the variable and exponent the same, resulting in 2 y 2 .
The correct statement is to subtract the coefficients ( 5 − 3 ) .
Explanation
Understanding the Expression We are asked to identify the correct statement when solving the expression 5 y 2 − 3 y 2 . This involves combining like terms, which means we need to look at the coefficients and exponents of the variable y .
Identifying Like Terms The expression 5 y 2 − 3 y 2 contains like terms because both terms have the same variable, y , raised to the same power, which is 2. To simplify the expression, we combine the coefficients of the like terms. The coefficients are 5 and -3.
Combining Like Terms To combine the like terms, we subtract the coefficients: 5 − 3 = 2 . Therefore, 5 y 2 − 3 y 2 = 2 y 2 . This means we subtract the coefficients and keep the variable and exponent the same.
Evaluating the Statements Now, let's examine the given statements:
Add the coefficients ( 5 + 3 ) : This is incorrect because we need to subtract the coefficients, not add them.
Add the exponents ( 2 + 2 ) : This is incorrect because we only combine like terms by adding or subtracting the coefficients, not the exponents.
Subtract the exponents ( 2 − 2 ) : This is incorrect for the same reason as above; we don't subtract the exponents.
Subtract the coefficients ( 5 − 3 ) : This is the correct statement because we subtract the coefficients to combine the like terms.
Final Answer The correct statement is: Subtract the coefficients ( 5 − 3 ) .
Examples
When calculating the area of a garden, you might find yourself needing to combine like terms. For example, if you have two rectangular sections of the garden with the same width ( y ) and lengths 5 y and 3 y , the total area can be expressed as 5 y 2 + 3 y 2 . Combining these like terms simplifies the calculation, making it easier to determine the total area: 5 y 2 + 3 y 2 = 8 y 2 . This principle applies to various scenarios involving areas, volumes, and other quantities in real-world applications.
