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:

$\frac{1}{5}x-\frac{1}{2}$

and

$5x-\frac{5}{6}$

So, we can write:

$(\frac{1}{5}x-\frac{1}{2})\cdot(5x-\frac{5}{6})$

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:

$x^2-\frac{x}{6}-\frac{5}{2}x+\frac{5}{12}$

We simplify as we can:

$x^2-\frac{8}{3}x+\frac{5}{12}$

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

$x^2-\frac{8}{3}x+\frac{5}{12}$