Find the sum and the difference of the following expressions

a + b and a - b

The sum of both expressions a + b and a - b is 2a

The difference of a + b and a - b is 2b

Solution:

Given expression is: a + b and a - b

To find: sum and the difference of expressions

Sum means we have to add both expressions and we use the symbol "+"

In mathematics, sum can be defined as the result or answer we get on adding two or more numbers or terms or expressions

Sum of a + b and a - b

Sum = a + b + (a - b)

On removing the brackets,

Sum = a + b + a - b

b and - b gets cancel each other

Sum = a + a = 2a

Thus the sum of both expressions is 2a

Difference of a + b and a - b

Difference means we have to subtract the expression a + b and a - b and we use the symbol "-"

Difference = a + b - (a - b)

On removing the brackets,

There are two simple rules to remember: When you multiply a negative number by a positive number then the product is always negative. When you multiply two negative numbers or two positive numbers then the product is always positive.

Difference = a + b - a + b

a and - a gets cancel each other

Difference = 2b

Thus the difference of both expressions is 2b