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We begin by addressing the parenthesis first:
Remember that:
When we multiply a positive number by a negative number the result will be negative.
When we multiply a negative number by a negative number the result will be positive.
Hence we obtain the following calculation:
Next we join together the a coefficients:
We then join together the b coefficients:
We obtain the following:
\( 100-(5+55)= \)
The negative sign acts like multiplying by -1. When you multiply (a-b) by -1, you get -1×a + (-1)×(-b) = -a + b. The negative times negative gives positive!
Think of it as opposite day! Every sign inside the parentheses becomes its opposite when you have a minus sign in front. Positive becomes negative, negative becomes positive.
The same rule applies! For example: . Every single term gets its sign flipped.
You could, but it's riskier! Working with parentheses first (following order of operations) prevents sign errors and makes the algebra much cleaner.
Because we have and , which are additive inverses. They always add up to zero: .
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