If a and b are integers, what is the sum of a+b+(-b). explain how?
since b+(-b) = 0, the sum is just a+0 = a
read about additive inverse and identity.
It's 0+a because b+(-b) is 0
To find the sum of a+b+(-b), we can simplify the expression step by step.
1. Start with the expression: a+b+(-b).
2. The term (-b) can be rewritten as (-1)b, since multiplying a number by -1 gives its additive inverse.
3. Applying the distributive property, we get: a+b+(-1)b.
4. Grouping like terms, we have: (a+b)+(-1)b.
5. We can then simplify further by combining the terms within the parentheses: a+b+(-1)b = a+(b+(-1)b).
6. According to the associative property of addition, we can rearrange the parentheses: a+(b+(-1)b) = a+(b-b).
7. Since b-b equals zero, our simplified expression becomes: a+0.
8. The sum of any number and zero is equal to the original number. Therefore, a+0 equals a.
9. Therefore, the sum of a+b+(-b) is equal to a.
In conclusion, the sum of a+b+(-b) simplifies to a.
To find the sum of a+b+(-b), we can simplify the expression by combining like terms.
The expression is a+b+(-b). The parentheses around -b indicate that we need to negate the value of b. Negating a value means changing its sign from positive to negative or vice versa.
So, (-b) means the negative value of b. Therefore, the expression can be simplified as a+b-b.
When we have a positive value (+b) and subtract a negative value (-b), it is the same as adding the positive value (+b). Thus, a-b+b simplifies to a.
Therefore, the sum of a+b+(-b) is equal to a.