The distributive property states the following:
[tex]a\cdot(b+c)=a\cdot b+a\cdot c[/tex]So in order to decompose the expression 8 * 78, we can decompose the number 78 in any two numbers that when added are equal 78:
[tex]\begin{gathered} 8\cdot(40+38) \\ 8\cdot(1+77) \\ 8\cdot(39+39) \end{gathered}[/tex]For each case, let's show using the distributive property that the result is the same:
[tex]\begin{gathered} 8\cdot78=624 \\ \\ 8\cdot(40+38)=8\cdot40+8\cdot38=320+304=624 \\ 8\cdot(1+77)=8\cdot1+8\cdot77=8+616=624 \\ 8\cdot(39+39)=8\cdot39+8\cdot39=312+312=624 \end{gathered}[/tex]