Respuesta :
Step 1
Given
[tex]-2(3n+5)+4(2n+3)_{}[/tex]Required; to use the distributive property to write an equivalent expression
Step 2
State the distributive property (distributive law)
[tex]\begin{gathered} a(b+c)\text{ = ab + ac} \\ or \\ a(b-c)=ab-ac \\ \text{where a,b and c are real numbers} \end{gathered}[/tex]Step 2
Apply the property to the question at hand.
[tex]\begin{gathered} we\text{ will start with the first part : (-2(3n+5))} \\ \text{-2(3n+5) =(-2(3n)) + (-2(5)) } \end{gathered}[/tex][tex]\begin{gathered} \text{Then the second part ; (4(2n+3))} \\ 4(2n+3)=(4(2n))\text{ + (4(3))} \end{gathered}[/tex]Step 3
Write the full equivalent expression
[tex]\lbrack-2(3n)+(-2(5))\text{ \rbrack+\lbrack}4(2n)+4(3)\rbrack[/tex]Hence
[tex]-2(3n+5)+4(2n+3)\text{ = }\lbrack-2(3n)+(-2(5))\text{ \rbrack+\lbrack}4(2n)+4(3)\rbrack[/tex][tex]\begin{gathered} \lbrack-2(3n)+(-2(5))\text{ \rbrack+\lbrack}4(2n)+4(3)\rbrack\text{ = -6n +(-10)+8n+12} \\ \lbrack-2(3n)+(-2(5))\text{ \rbrack+\lbrack}4(2n)+4(3)\rbrack=\text{ }-6n+8n-10+12 \\ \lbrack-2(3n)+(-2(5))\text{ \rbrack+\lbrack}4(2n)+4(3)\rbrack=2n+2 \end{gathered}[/tex]Hence
[tex]-2(3n+5)+4(2n+3)\text{ = 2n+2}[/tex]Answer = 2n+2
