Question

Someone help me understand this step by step please.​

Answer 1

`(s \bullet{}t)(x) = \boxed{ {3x}^(2) + 8x + 4 } \\(s + t)(x) = \boxed{ 4x + 4}\\ (s - t)(x) = \boxed{- 2x}`

Explanation:

`if \: \to \\ \to \: s(x) =x + 2 \\ \to \: t(x) =3x + 2 \\ find \: the \: various \: expressions \to \\ 1. \to(s \bullet{}t)(x) \\ 2. \to(s + t)(x) \\ 3. \to(s - t)(x) \\ \\ \boxed{ \underline{expression \: 1.}} \\ (s \bullet{}t)(x) = (x + 2)(3x + 2) \\ (s \bullet{}t)(x) = {3x }^(2) + 2x + 6x + 4 \\ \underline{(s \bullet{}t)(x) = {3x}^(2) + 8x + 4} \\ \\ \boxed{ \underline{expression \: 2.}} \\(s + t)(x) = (x + 2) + (3x + 2) \\(s + t)(x) = {3x } + x +2 + 2\\ \underline{(s + t)(x) = 4x + 4} \\ \\ \boxed{ \underline{expression \: 3.}} \\ (s - t)(x) = (x + 2) - (3x + 2) \\(s - t)(x) = x +2 -3x - 2\\ \underline{(s - t)(x) = - 2x}`

♨Rage♨

Answer 2

Explanation:

(s*t)(x) = (x+2)(3x+2)

Using the Associative Property of Multiplication, we get

(s*t)(x) = 3x²+2x+6x+4 = 3x²+8x+4

For (s+t)(x), we just add the two to get 4x+4

For (s-t)(x), we subtract t from s to get -2x. Plugging -1 in for x, we get -2(-1)=2