Question

If \[A = \left( {16x + 8} \right) + 4\] and \[B = \left( {15x - 10} \right) + \left( { - 5} \right)\] then \[A - B\] is ____.

Answer 1

Hint: By algebraic calculations we know that we can only add or subtract the like terms. Here we are going to directly apply this rule to get a solution.

Complete step by step solution:
From the question, it is given that \[A = \left( {16x + 8} \right) + 4\] and \[B = \left( {15x - 10} \right) + \left( { - 5} \right)\]
Now we have two equations First we are going to Simplify ‘$A$’ and then ‘$B$’.
Now let us consider the equation ‘$A$’.
\[ \Rightarrow A = \left( {16x + 8} \right) + 4\]
Now we are going to add only like terms. Here \[16x\] has a variable \[x\] so we cannot add or subtract the other numbers to \[16x\]. So first we are going to add the numbers in the equation \[A = \left( {16x + 8} \right) + 4\]
In the equation \[A = \left( {16x + 8} \right) + 4\] , \[8\] and \[4\] numbers that we are going to add \[8 + 4 = 12\].
After adding the like terms, we have \[A = 16x + 12\]
Now let us consider the equation ‘$B$’.
\[ \Rightarrow B = \left( {15x - 10} \right) + \left( { - 5} \right)\]
We are going to proceed the same procedure for the equation ‘$B$’
Here \[15x\] has a variable \[x\] so we cannot add or subtract the other numbers to \[15x\]
In the equation \[B = \left( {15x - 10} \right) + \left( { - 5} \right)\], \[ - 10\] and \[ - 5\] are numbers that we are going to add. \[\left( {-10} \right) + \left( { - 5} \right) = - 15\]
After adding the like terms, we have \[B = 15x - 15\]
Now we have the simplified forms of ‘$A$’ and ‘$B$’.
Now our aim is to find the difference between $A$ and $B$ that is \[A - B\]. Hence we are going to substitute the value of ‘$A$’ and ‘$B$’.
\[ \Rightarrow A - B = 16x + 12 - (15x - 15)\]
\[ \Rightarrow A - B = 16x + 12 - 15x + 15\]
Now we are going to add and subtract only the like terms. Here \[15\] and \[12\] are numbers, \[16x\] and \[15x\] are variables.
Therefore, \[A - B = (16x - 15x) + 12 + 15\]
Now we are going to subtract the variable terms \[16x - 15x = x\] and then add the numbers \[12 + 15 = 27\].
Hence we finally found that, \[A - B = x + 27\]

The value of \[A - B = x + 27\].

Note:
Don’t get confused while doing simple calculations like addition and subtraction. When we are going to add or subtract like terms, the coefficients are added or subtracted. The variable term remains unchanged.