Find the product. Write any variables in alphabetical order. (2q+5r)(2q−5r)2𝑞+5𝑟2𝑞-5𝑟

1. Break Down the Problem

We need to find the product of the expression $(2q + 5r)(2q - 5r)$. This expression can be solved using the difference of squares formula, which is given as: $a^2 - b^2 = (a + b)(a - b)$ In our case, we can identify $a = 2q$ and $b = 5r$.

2. Relevant Concepts

Using the difference of squares formula, we can rewrite the expression as: $(2q + 5r)(2q - 5r) = (2q)^2 - (5r)^2$

3. Analysis and Detail

Now, we will calculate $(2q)^2$ and $(5r)^2$:

1. Calculate $(2q)^2$: $(2q)^2 = 4q^2$
2. Calculate $(5r)^2$: $(5r)^2 = 25r^2$ Now substitute back into the equation: $(2q + 5r)(2q - 5r) = 4q^2 - 25r^2$

4. Verify and Summarize

We have derived the expression step by step. The difference of squares was applicable, and both squares were calculated correctly.

Final Answer

The product of $(2q + 5r)(2q - 5r)$ is: $4q^2 - 25r^2$