Answer :

GinnyAnswer
To multiply and simplify the expression [tex]\((6 + 6t)^2\)[/tex], we can use the binomial theorem or simply expand it using the distributive property (also known as the FOIL method). Let's go through it step-by-step:

### Binomial Theorem Approach:
The binomial theorem states:
[tex]\[ (a + b)^2 = a^2 + 2ab + b^2 \][/tex]
In this case, [tex]\(a = 6\)[/tex] and [tex]\(b = 6t\)[/tex].

1. Calculate [tex]\(a^2\)[/tex]:
[tex]\[ 6^2 = 36 \][/tex]

2. Calculate [tex]\(2ab\)[/tex]:
[tex]\[ 2 \cdot 6 \cdot 6t = 72t \][/tex]

3. Calculate [tex]\(b^2\)[/tex]:
[tex]\[ (6t)^2 = 36t^2 \][/tex]

### Putting it all together:
The expanded form is:
[tex]\[ 6^2 + 2 \cdot 6 \cdot 6t + (6t)^2 = 36 + 72t + 36t^2 \][/tex]

Therefore,
[tex]\[ (6 + 6t)^2 = 36 + 72t + 36t^2 \][/tex]

### Final Answer:
[tex]\[ \boxed{36 + 72t + 36t^2} \][/tex]

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