Answer:
[tex]\boxed {\boxed {\sf 6x^2+7x-20}}}[/tex]
Step-by-step explanation:
We are given 2 binomials (meaning they have 2 terms) and asked to express as a trinomial.
To do this, we have to multiply the 2 binomials using the FOIL method. FOIL stands for first, outside, inside, and last. Basically, multiply the first terms from both, then the outside, and so on.
F : First
[tex](\underline{2x}+5)(\underline{3x}-4)[/tex]
2x * 3x= 6x²
O: Outside
[tex](\underline{2x}+5)(3x \underline {-4})[/tex]
2x * -4 = -8x
I: Inside
[tex](2x+\underline5)(\underline{3x}-4)[/tex]
5 *3x=15x
L: Last
[tex](2x+\underline5)(3x\underline{-4})[/tex]
5*-4= -20
Now, put all the products together into one expression.
[tex]6x^2-8x+15x-20[/tex]
However, this is not a trinomial yet. There are like terms that can be combined. Notice how 2 terms both have the variable x. They can be added together.
[tex]6x^2 + (-8x+15x)-20[/tex]
[tex]6x^2+7x-20[/tex]
Now there are 3 terms and we have a trinomial: 6x²+7x-20
