Question

The value of the expression, \[A-\left( A-B \right)\] .

Answer 1

Hint: Assume that \[A=5\] and \[B=6\] . Now, put the numerical value of A and B in the expression, \[A-\left( A-B \right)\] . Use the property that the multiplication of two negative numerical terms results in a positive numerical term. Expand the given expression and then calculate the numerical value. Now, compare the numerical value of the expression with the numerical value of A and B.

Complete step-by-step answer:
According to the question, we are given an expression and we have to simplify it.
\[A-\left( A-B \right)\] …………………………………(1)
First of all, let us assume that the numerical value of A is 5 and the numerical value of B is 6 i.e,
\[A=5\] ………………………………………(2)
\[B=6\] ………………………………………(3)
Now, using equation (2) and equation (3), and substituting A by 5 and B by 6 in equation (1), we get
\[=5-\left( 5-6 \right)\] ……………………………..(4)
On expanding equation (4), we get
\[=5-\left( 5-6 \right)\]
\[=5-5+\left( -1 \right)\left( -6 \right)\] ………………………………………..(5)
We know the property that the multiplication of two negative numerical terms results in a positive numerical term ………………………………………….(6)
Now, applying the property shown in equation (6) and on simplifying equation (5), we get
\[=5-5+6\]
\[=6\] ……………………………………..(7)
Now, from equation (3), we have the numerical value of B which is equal to 6. So, we can replace 6 by B.
On substituting 6 by B in equation (7), we get
\[=6\]
\[=B\] …………………………………………..(8)
From equation (8), we have got the value of the given expression that is equal to B
Therefore, the value of the given expression is B.

Note: We can also solve this question without assuming the numerical value of A and B. Just expand the given expression by using the property that the multiplication of two negative numerical terms results in a positive numerical term. Now, the expression can be solved easily, \[A-A+B=B\] .