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

Question

Express the following exercise as a sum and as a power:

$(7b+3z)(7b+3z)=\text{?}$

00:00 Express as sum and power

00:04 Double factor itself is actually squared

00:14 Use this formula and square it

00:22 Use shortened multiplication formulas to open the parentheses

00:36 When 7B is A

00:39 And 3Z is B

00:44 We'll substitute according to the formula and solve

00:54 Solve the squares and multiplications

01:06 And this is the solution to the question

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:

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:

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

$(7b+3z)^2$

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

$(7b+3z)^2$