Problem 50 - College Algebra Essentials

Question

Find each product. $$(9-5 x)^{2}$$

Step-by-Step Solution

Answer

So, \((9-5x)^2 = 25x^2 - 90x + 81\)

Step 1: Identify a and b

In the given binomial \((9-5x)^2\), \(a=9\) and \(b=5x\). So, it can be written using the formula as \(a^2 - 2ab + b^2\).

Step 2: Apply the formula

Applying the formula: \(a^2 - 2ab + b^2 = (9)^2 - 2*(9)*(5x) + (5x)^2\). This simplifies to \(81 - 90x + 25x^2\).

Step 3: Arrange in standard polynomial form

Most generally, polynomial expressions are written in descending order of powers. So, rearranging our answer gives us: \(25x^2 - 90x + 81\)