Simplify the following expression:

-3 + 4(a - 3b + 2) - 5(2 - a + 3b)

Options:
1) 3a - 9b - 5
2) 3a - b - 11
3) 9a - 27b - 5
4) -a + 3b - 5

To simplify the expression − 3 + 4 ( a − 3 b + 2 ) − 5 ( 2 − a + 3 b ) , follow these steps:

Distribute the Constants into the Parentheses :


First, distribute the 4 in the expression 4 ( a − 3 b + 2 ) :
4 ( a − 3 b + 2 ) = 4 a − 12 b + 8

Next, distribute the -5 in the expression − 5 ( 2 − a + 3 b ) :
− 5 ( 2 − a + 3 b ) = − 10 + 5 a − 15 b



Combine All Parts of the Expression :
The expression now becomes:


− 3 + ( 4 a − 12 b + 8 ) − ( 10 − 5 a + 15 b ) Simplify this to: − 3 + 4 a − 12 b + 8 − 10 + 5 a − 15 b

Combine Like Terms :


Combine the a terms: 4 a + 5 a = 9 a

Combine the b terms: − 12 b − 15 b = − 27 b

Combine the constant terms: − 3 + 8 − 10 = − 5
So, the simplified expression is:


9 a − 27 b − 5
Now, compare this result with the options given:
Options:

3 a − 9 b − 5

3 a − b − 11

9 a − 27 b − 5

− a + 3 b − 5


The correct option is 3) 9 a − 27 b − 5 .

Answered by LiamAlexanderSmith | 2025-07-22

The simplified expression of the given mathematical expression is 9 a − 27 b − 5 . Among the options provided, the correct choice is option 3. This is done by distributing constants, combining like terms, and simplifying step-by-step.
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Answered by LiamAlexanderSmith | 2025-08-05