Question

Subtract (a − b) from (a + b).

Answer 1

Hint:x − y is read as "x minus y" which means "subtract y from x". For distinct x and y, the statements x − y
and y − x have the same magnitude but opposite signs, and hence they must not be confused with each other.

Recall that $-(a\pm b)$ = $-a\mp b$ . It means that the negative of a sum / difference is the sum / difference of the quantities with the signs reversed.

Complete step by step solution:
The statement "subtract x from y" is mathematically written as x − y.
Therefore, "subtract (a − b) from (a + b)" is mathematically equivalent to:
(a + b) − (a − b)

Which can be written as:
= (a + b) − [a + (−b)]

On expanding the brackets, we get:
= a + b − a − (−b)
= a + b − a + b
= 2b, which is the required answer.

Note:Instead, (a − b) − (a + b) = −2b, which is "subtracting (a + b) from (a − b)". Always pay close attention to the limiting and conditional words like: only, by, from, to, per, each, of, at least, all, exactly etc. They define the type of relation between the quantities.

Symbols mean the same thing as they are spoken. For instance, a ÷ b means "a is divided by b".

The order of the numbers is very important when subtracting or dividing. Usually, it doesn't matter in case of addition / multiplication.