Question

Express the product of (1/5x + 1) and (1/6x + 5/4) as a trinomial in simplest form

Answer 1

`((1)/(5)x+1)((1)/(6)x+(5)/(4))`

Use distributive property to remove the parentheses:

`(a+b)(c+d)=ac+ad+bc+bd`
`\begin{gathered} =(1)/(5)x*(1)/(6)x+(1)/(5)x*(5)/(4)+1*(1)/(6)x+1*(5)/(4) \\ \\ Multiplication\text{ }of\text{ }fractions: \\ (a)/(b)*(c)/(d)=(a*c)/(b*d) \\ \\ =(1)/(30)x^2+(5)/(20)x+(1)/(6)x+(5)/(4) \\ \\ =(1)/(30)x^2+(1)/(4)x+(1)/(6)x+(5)/(4) \\ \\ Addition\text{ }of\text{ }fractions: \\ (a)/(b)+(c)/(d)=(ad+bc)/(bd) \\ \\ =(1)/(30)x^2+((6x+4x)/(24))+(5)/(4) \\ \\ =(1)/(30)x^2+(10)/(24)x+(5)/(4) \\ \\ Simplify: \\ =(1)/(30)x^2+(5)/(12)x+(5)/(4) \end{gathered}`Then, the product in the simplest form is:
`(1)/(30)x^2+(5)/(12)x+(5)/(4)`