Question

How do you factor $2ac+ad+6bc+3bd$?

Answer 1

Hint: For this problem we need to calculate the factors of the given equation. We can observe that the given equation is a polynomial having four variables which are $a$, $b$, $c$, $d$. We will first observe the given equation and take the appropriate terms according to our convenience and simplify the equation to get the factors of the given equation, which is our required result.

Complete step by step solution:
Given equation, $2ac+ad+6bc+3bd$.
We can observe that the given equation is a polynomial which is having four variables $a$, $b$, $c$, $d$. In the given equation we have the common term $a$ in first two terms. So, we are taking $a$ as common from the first two terms, then we will get
$\Rightarrow 2ac+ad+6bc+3bd=a\left( 2c+d \right)+6bc+3bd$
Now in the above equation we can observe that $3b$ can be taken as common from the last two terms. Hence taking $3b$ as common from the last two terms, then we will have
$\Rightarrow 2ac+ad+6bc+3bd=a\left( 2c+d \right)+3b\left( 2c+d \right)$
Again, in the above equation we can observe the common term $2c+d$. So, taking $2c+d$ as common from the above equation, then we will get
$\Rightarrow 2ac+ad+6bc+3bd=\left( a+3b \right)\left( 2c+d \right)$
Hence the factors of the given equation $2ac+ad+6bc+3bd$ are $a+3b$, $2c+d$.

Note: We can also check whether the obtained solution is correct or wrong. When we multiply the calculated factors then we must get the given equation as result. Otherwise, the obtained factors are not correct.