Let's determine the hidden statement using the decoder. Here are our steps:
1. Identify the answers in A and B.
2. Match each of those answers to the corresponding letter in the decoder.
3. Write the matched statement next to each answer.
4. Concatenate these statements to reveal the hidden statement.
Given answers are:
1. [tex]$A$[/tex]
2. [tex]$R$[/tex]
3. [tex]$L$[/tex]
4. [tex]$S$[/tex]
5. [tex]$H$[/tex]
6. [tex]$T$[/tex]
### Step-by-Step Matching:
1. Answer: [tex]$A$[/tex]
- Decoder: [tex]$A = 20 a b(2 a+3 b)$[/tex]
2. Answer: [tex]$R$[/tex]
- Decoder: [tex]$R = 9 x y(2-y+4 x)$[/tex]
3. Answer: [tex]$L$[/tex]
- Decoder: [tex]$L = a b c$[/tex]
4. Answer: [tex]$S$[/tex]
- Decoder: [tex]$S = (b+1)$[/tex]
5. Answer: [tex]$H$[/tex]
- Decoder: [tex]$H = a-b^2$[/tex]
6. Answer: [tex]$T$[/tex]
- Decoder: [tex]$T = 4 x(x^2+x+1)$[/tex]
### Hidden Statement
Next, we concatenate the matched statements in the order of the answers:
1. [tex]$20 a b(2 a+3 b)$[/tex]
2. [tex]$9 x y(2-y+4 x)$[/tex]
3. [tex]$a b c$[/tex]
4. [tex]$(b+1)$[/tex]
5. [tex]$a-b^2$[/tex]
6. [tex]$4 x(x^2+x+1)$[/tex]
By putting these together in order, we get the hidden statement:
[tex]\[ 20 a b(2 a+3 b)9 x y(2-y+4 x)a b c(b+1)a-b^24 x(x^2+x+1) \][/tex]
Thus, the hidden statement is:
[tex]\[ \boxed{20 a b(2 a+3 b)9 x y(2-y+4 x)a b c(b+1)a-b^24 x(x^2+x+1)} \][/tex]
