How do you simplify $3\left( 5a+6b \right)+8\left( 2a-b \right)$ ?

Hint: To simplify $3\left( 5a+6b \right)+8\left( 2a-b \right)$ , we will apply the distributive property on the two terms. Let us consider $a\left( b+c \right)$ . We have to multiply a to both b and c along with its sign, that is, $a\left( b+c \right)=ab+ac$ . This is distributive property. After applying this property on to the given expression, then we will have to simplify it to get the required answer.

Complete step-by-step solution:
We need to simplify $3\left( 5a+6b \right)+8\left( 2a-b \right)$ . First we will apply the distributive property on the two terms. Before that, let us see what distributive property is.
Let us consider $a\left( b+c \right)$ . We have to multiply a to both b and c along with its sign.
$\Rightarrow a\left( b+c \right)=ab+ac$
Now, let us consider the given expression $3\left( 5a+6b \right)+8\left( 2a-b \right)$ . When we apply the distributive property here, we will get
$\left( 3\times 5a+3\times 6b \right)+\left( 8\times 2a-8\times b \right)$
Let us solve this by doing the multiplication.
$\Rightarrow \left( 15a+18b \right)+\left( 16a-8b \right)$
Let us now remove the brackets to solve this expression easily.
$\Rightarrow 15a+18b+16a-8b$
Now, we will add the terms. The terms with similar variables will be added. We will get
$3\left( 5a+6b \right)+8\left( 2a-b \right)=31a+10b$
Hence, the answer is $31a+10b$ .

Note: Students must be careful when working with algebraic expressions. Minor mistakes can lead the entire solution to be wrong. Students must be thorough with the algebraic rules and properties. Note that we can add or subtract terms having the same variables only. This means that we cannot add a constant with a variable or add terms of different variables.