Hi, I'm happy to help!
To simplify this expression, we need to first use the order of operations <u>(Parenthesis, Exponents, Multiplication or Division (Left to Right), and Addition or Subtraction (Left to Right)</u>), then combine like terms. (<u>80,40,57</u>, or <u>6t, 8t, 98t</u>, or<u> 2t²,7t²,83t²</u>)
When a number is next to parenthesis with no sign, it means we are using multiplication. We can change this expression to look like this, by changing all the numbers next to the parenthesis with no sign, to one with a multiplication sign.
8(5+t) - 2(t+1)
8(5 + t) - 2(t+1)=
8×(5+t) - 2×(t+1)×
8×(5 + t) - 2×(t+1)=
We start with parenthesis and solve everything inside of those, but, because everything inside the parenthesis are unlike terms, we cannot combine them.
Next, We look for any exponents (x²). There are none in this equation.
We then look for multiplication or division. There is a lot of multiplication, so we start solving that from left to right.
8×(5+t) - 2×(t+1)×
8×(5 + t) - 2×(t+1)=
40+8t - 2×(t+1)×
8×(5 + t) - 2×(t+1)=
40+8t - 2×(t+1)×
8×(5 + t) - 2×(t+1)=
(40+8t) - (2t+2)×
8×(5 + t) - 2×(t+1)=
(40+8t) - (2t+2)×
8×(5 + t) - 2×(t+1)=
(40+8t) - (16t+16)×(5 + t) - 2×(t+1)=
(40+8t) - (16t+16)×(5 + t) - 2×(t+1)=
(40+8t) - (80t+16t²+80+16t) - 2×(t+1)=
(40+8t) - (80t+16t²+80+16t) - 2×(t+1)=
(40+8t) - (80t+16t²+80+16t) - (2t+2)=
(40+8t) - (80t+16t²+80+16t) - (2t+2)=
Now, before we do anything else, we need to recheck the parenthesis, now that they have changed. We can further simplify the middle parenthesis by adding together like terms.
(40+8t) - (80t+16t²+80+16t) - (2t+2)=
(40+8t) - ((80t+16t)+16t²+80) - (2t+2)=
(40+8t) - (96t+16t²+80) - (2t+2)=
(40+8t) - (96t+16t²+80) - (2t+2)=
Now, we look for addition or subtraction of like terms. We can now remove the parenthesis, since everything inside of the last two parenthesis is negative, we turn it negative, as long as we only combine the like terms.
40+8t - 96t-16t²-80 - 2t-2=
Once we find like terms, we can rearrange the expression.
(40-80-2)+8t - 96t+16t² - 2t
(-42)+8t - 96t-16t² - 2t
(-42)+8t - 96t-16t² - 2t
(-42)+(8t-96t-2t)-16t²
(-42)+(-90t)-16t²
(-42)+(-90t)-16t²
This doesn't have any like terms, so we don't alter it.
(122)+(-90t)-16t²
We can now remove the parenthesis.
122-90t-16t²
Since there are no more like terms this is the furthest we can simplify. We can then rearrange the expression to be arranged completely correct.
-16t²-90t-42
I hope this was helpful, keep learning! :D
where 
is the first term and d is the constant difference, 
,