Factor polynomials in the form 'a² + 2ab + b²'. Fill in the correct answers in the blanks for the provided expressions.

Steps to Solve

1. Identifying the form Recognize that we are working with expressions of the form $a^2 + 2ab + b^2$, which factors to $(a + b)^2$.

2. Rewriting the expression Write the polynomial in the standard form for perfect squares:

• For example, in the first problem $x^2 + 4x + 4$, identify $a = x$ and $b = 2$.

3. Substituting values Substitute into the identity:

• The expression $x^2 + 4x + 4$ can be recognized as $(x + 2)^2$.

4. Filling in the blanks For each problem:

• Fill in the appropriate blanks with the identified values for $a$ and $b$.

5. Factoring the remaining expressions Continue with the same steps for each additional expression:

• For the second problem $36 + 12x + x^2$, we can rearrange it as $x^2 + 12x + 36$ and identify $a = x$ and $b = 6$. So it's factorable as $(x + 6)^2$.

6. Applying to all expressions Repeat the process through problems 3 to 8 in the same way. Identify $a$ and $b$, fill in the factors, and write the factored form.