Simplify the following expression by combining like terms:
`-3\left(10b+10\right)+5\left(b+2\right)-6\left(b-2\right)+10-16b`
First, distribute the negative sign through the expression inside the parentheses:
-3 * 10b + -3 * 10
This simplifies to:
-30b - 30
Next, distribute the positive 5 through the expression inside the parentheses:
5 * b + 5 * 2
This simplifies to:
5b + 10
Next, distribute the negative 6 through the expression inside the parentheses:
-6 * b + -6 * -2
This simplifies to:
-6b + 12
Finally, combine like terms by adding/subtracting the terms with the same variables and their coefficients:
-30b - 30 + 5b + 10 - 6b + 12 + 10 - 16b
Combine the coefficient terms:
-30b + 5b - 6b - 16b - 30 + 10 + 12 + 10
This simplifies to:
-47b - 2
To simplify the expression `-3(10b+10)+5(b+2)-6(b-2)+10-16b`, we can start by distributing the coefficients to each term within the parentheses.
First, let's distribute `-3` to `10b` and `10`:
`-3 * 10b = -30b`
`-3 * 10 = -30`
So, the expression becomes:
`-30b - 30 + 5(b+2) - 6(b-2) + 10 - 16b`
Next, let's distribute `5` to `(b+2)`:
`5 * b = 5b`
`5 * 2 = 10`
So, the expression becomes:
`-30b - 30 + 5b + 10 - 6(b-2) + 10 - 16b`
Now, let's distribute `-6` to `(b-2)`:
`-6 * b = -6b`
`-6 * -2 = 12`
So, the expression becomes:
`-30b - 30 + 5b + 10 - 6b + 12 + 10 - 16b`
Now, we can combine like terms by adding or subtracting coefficients of the same variable `b`:
Combining `-30b`, `5b`, and `-6b`, we get `-30b + 5b - 6b = -31b`
Combining the constant terms `-30`, `10`, `12`, and `10`, we get `-30 + 10 + 12 + 10 = -32`
Thus, the simplified expression is `-31b - 32`.