Theory:

The distributive property states that multiplying a sum by a number gives the same result as multiplying each subtracted by the number and then subtracting the products together.
For any number \(a\), \(b\) and \(c\), we have \(a × b - c = a × b - a × c\).
 
Consider the number \(4\), \(3\) and \(2\) we have
 
\(4 × 3 - 2 = 4 × 3 - 4 × 2\). (LHS \(=\) RHS)
 
LHS: \(4\) \(×\) \(2 - 3\) \(=\) \(4\) \(×\) \(1\)
 
\(=\) \(4\).
 
RHS: \(4\) \(×\) \(3\) \(-\) \(4\) \(×\) \(2\)
 
\(=\) \(12\) \(-\) \(8\)
 
\(=\) \(4\).
 
Thus, \(4\) \(×\) \(3 - 2\) \(=\) \(4\) \(×\) \(3\) \(-\) \(4\) \(×\) \(2\). (LHS \(=\) RHS)
  
For any three rational numbers ab, cd and ef, we have ab \(×\) cdef \(=\) ab×cd \(-\) ab×ef.
 
Consider the rational numbers 3423 and 76 we have
 
 
34 \(×\) {2376}  \(=\) 34×23 \(-\) 34×76. (LHS \(=\) RHS)
 
LHS: 34 \(×\) {2376}
 
34 \(×\) {2376} \(=\) 34 \(×\) {(47)6}
 
\(=\) 34 \(×\) 116 \(=\) 3324.
 
RHS34×23 \(-\) 34×76
 
34×23 \(=\) 3×24×3 \(=\) 612 \(=\) 12.
 
And 34×76 \(=\) 2124.
 
Therefore 34×23 \(+\) 34×76 \(=\) 12 \(-\) 2124 \(=\) 3324.
 
Thus, 34 \(×\) {2376} \(=\) 34×23 \(+\) 34×76. (LHS \(=\) RHS)