What is 8b - ab + 7 subtracted from 3a - 9ab + b?

What is 8b - ab + 7 subtracted from 3a - 9ab + b?

• A. -4a - 8ab - 7b
• B. -5a + 7ab + 8b
• C. 5a + 8ab + 7b
• D. -2a + 8ab - 7b

Answer: (A)

To find the correct solution, first we need to correctly execute the operation of subtraction indicated in the problem, which requires us to subtract the expression \( 8b - ab + 7 \) from \( 3a - 9ab + b \). Start by rewriting the subtraction: \[ (3a - 9ab + b) - (8b - ab + 7) \] Distributing the minus sign to the second expression gives us: \[ 3a - 9ab + b - 8b + ab - 7 \] Now, combine the like terms step-by-step: 1. For the \( a \) terms, we have: \[ 3a \] 2. For the \( ab \) terms, combine \( -9ab \) and \( ab \): \[ -9ab + ab = -8ab \] 3. For the \( b \) terms, combine \( b \) and \( -8b \): \[ b - 8b = -7b \] 4. Finally, include the constant term, which is \( -7 \). Now, putting all those results together, we form the complete expression:

To find the correct solution, first we need to correctly execute the operation of subtraction indicated in the problem, which requires us to subtract the expression ( 8b - ab + 7 ) from ( 3a - 9ab + b ).

Start by rewriting the subtraction:

[ (3a - 9ab + b) - (8b - ab + 7) ]

Distributing the minus sign to the second expression gives us:

[ 3a - 9ab + b - 8b + ab - 7 ]

Now, combine the like terms step-by-step:

1. For the ( a ) terms, we have:

[ 3a ]

2. For the ( ab ) terms, combine ( -9ab ) and ( ab ):

[ -9ab + ab = -8ab ]

3. For the ( b ) terms, combine ( b ) and ( -8b ):

[ b - 8b = -7b ]

4. Finally, include the constant term, which is ( -7 ).

Now, putting all those results together, we form the complete expression: