Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Subtract the binomials.


On simplifying (-3y2 − 8) − (-5y2 + 1), we get ----------


y2 − ------
. Lines are for the two answers

Answer 1

Subtract the binomials by changing signs accordingly and combining like terms, resulting in 2y² - 9. Verify that the subtraction and combination are done correctly to ensure the answer is reasonable.

Step-by-step explanation:

To subtract the binomials, first distribute the negative sign to the terms in the second binomial. This is the simplification step: (-3y2 − 8) − (-5y2 + 1) becomes -3y2 − 8 + 5y2 − 1.

Next, combine like terms. Add the coefficients of the terms with y2: -3y2 + 5y2 = 2y2. Then, combine the constant terms: -8 − 1 = -9. So the result is 2y2 - 9.

To check if the answer is reasonable, we verify if like terms were correctly combined and the subtraction was applied accurately. In this case, the signs were appropriately changed, and like terms were combined correctly, which confirms that 2y2 - 9 is reasonable.

Answer 2

After subtracting and simplifying the binomials (-3y^2 - 8) and (-5y^2 + 1), the resulting expression is 2y^2 - 9.

Step-by-step explanation:

To subtract the binomials (-3y2 − 8) and (-5y2 + 1), we will first remove the parentheses and change the signs for the terms inside the second set of parentheses due to the minus sign in front of it. This means that we will be changing -5y2 to +5y2 and +1 to -1:

(-3y2 − 8) − (-5y2 + 1) = -3y2 − 8 + 5y2 - 1

Next, we combine like terms by adding the coefficients of the y2 terms and combining the constant terms:

-3y2 + 5y2 = 2y2
−8 − 1 = −9

So, after simplifying, the expression becomes:

2y2 − 9

After reviewing, this answer seems reasonable because the like terms have been correctly combined, and the correct signs have been applied during the subtraction.