Expand (7b+3z)²: Converting Between Power and Sum Notations

To express the given expression $(7b+3z)(7b+3z)$ as a sum and a power, we will follow these steps:

• Step 1: Identify the components as a binomial expansion:
  Let $a = 7b$ and $b = 3z$.
• Step 2: Use the formula for the square of a binomial, which is $(a+b)^2 = a^2 + 2ab + b^2$.
• Step 3: Calculate each term:
• $a^2 = (7b)^2 = 49b^2$
• $b^2 = (3z)^2 = 9z^2$
• $2ab = 2(7b)(3z) = 42bz$

By substituting these into the formula, we get:
$(7b+3z)^2 = 49b^2 + 2(7b)(3z) + 9z^2$

Therefore, the expression as a sum is $49b^2 + 42bz + 9z^2$, and as a power, it is $(7b+3z)^2$.

Thus, the solution to the problem is:

$49b^2 + 42bz + 9z^2$

$(7b+3z)^2$