Question

Express the product of (1/5x- 1/2) and (5x -5/6) as a trinomial in simplest form

Answer 1

We need to find the product of the expressions:

`(1)/(5)x-(1)/(2)`

and

`5x-(5)/(6)`

So, we can write:

`((1)/(5)x-(1)/(2))\cdot(5x-(5)/(6))`

Remember that when we have a product of two expressions that have two terms as:

`(a+b)\cdot(c+d)`

We can distribute it multiplicating as:

Then distributing our expressions we have:

`x^2-(x)/(6)-(5)/(2)x+(5)/(12)`

We simplify as we can:

`x^2-(8)/(3)x+(5)/(12)`

And it is the simplest form because it is not a perfect trinomial, we can conclude the correct answer is:

`x^2-(8)/(3)x+(5)/(12)`