Question

Find the product. $$\left(6 z+\frac{1}{3}\right)^{2}$$

Short answer

The product is \(36z^2 + 4z + \frac{1}{9}\).

Step-by-step solution

Identify the Binomial Terms

From the binomial \(6z + \frac{1}{3}\), identify the first term (a) as \(6z\) and the second term (b) as \(\frac{1}{3}\).

Apply Binomial Square Formula

Substitute \(6z\) and \(\frac{1}{3}\) into the formula for the square of a binomial \(a^2 + 2ab + b^2\). That gives us \((6z)^2 + 2*6z*\frac{1}{3} + (\frac{1}{3})^2\).

Simplify the Expression

Simplify the expression to give the final answer. This amounts to: \(36z^2 + 4z + \frac{1}{9}\).