Question

How do you use the distributive property to factor $10g^{2}h^{2}+9gh^{2}-g^{2}h$?

Answer 1

Hint: In order to solve this question, you should know what a distributive property is. Distributive property states that $ \left( a+b \right)\left( c+d \right)\text{ }=\text{ }ac+ad+bc+bd$. So here you need to apply the distributive property but in the reverse order. First you need to find out the term which is common in all the smaller terms in the equation. Then you need to take it out as common. Then, you get your final answer.

Complete step by step solution:
Here is the step wise solution. In this, the first step is to find out which term is common for all the terms in the given equation in the question. We can clearly see that the term $gh$ is common in all the terms in the equation.
The next step to do is to take it out as common from all the terms. If we take it out, we get the equation as
$\Rightarrow 10gh+9h-g$
Now we have to multiply the $gh$ term to the total of the above term to get the final answer, therefore, we get the answer as
$\Rightarrow gh\left(10gh+9h-g\right)$

Therefore, we get the final answer for the question, how do you use the distributive property to factor $10g^{2}h^{2}+9gh^{2}-g^{2}h$ as $ gh\left(10gh+9h-g\right)$.

Note: You can verify this question, by using the distributive property where you can multiply the $gh$ term to all the terms inside the bracket and see if it matches the original equation in the question. You need to remember the distributive property as it is a very important one.