Question

-2(3n+5)+4(2n+3)Use the Distributive Property towrite an equivalent expression

Answer 1

Step 1

Given

`-2(3n+5)+4(2n+3)_{}`

Required; to use the distributive property to write an equivalent expression

Step 2

State the distributive property (distributive law)

`\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}`

Step 2

Apply the property to the question at hand.

`\begin{gathered} we\text{ will start with the first part : (-2(3n+5))} \\ \text{-2(3n+5) =(-2(3n)) + (-2(5)) } \end{gathered}`
`\begin{gathered} \text{Then the second part ; (4(2n+3))} \\ 4(2n+3)=(4(2n))\text{ + (4(3))} \end{gathered}`

Step 3

Write the full equivalent expression

`\lbrack-2(3n)+(-2(5))\text{ \rbrack+\lbrack}4(2n)+4(3)\rbrack`

Hence

`-2(3n+5)+4(2n+3)\text{ = }\lbrack-2(3n)+(-2(5))\text{ \rbrack+\lbrack}4(2n)+4(3)\rbrack`
`\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}`

Hence

`-2(3n+5)+4(2n+3)\text{ = 2n+2}`

Answer = 2n+2