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Chapter 0: Problem 50

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

Short Answer

Expert verified
The product of squaring the binomial (9 - 5x) is \(25x^2 - 90x + 81\).

Step by step solution

01

Identify the binomial to be squared

The binomial given in the exercise is (9 - 5x).
02

Multiply the binomial by itself

To square this binomial, it must be multiplied by itself. i.e., (9 - 5x) * (9 - 5x).
03

Apply the FOIL method

The FOIL method stands for First, Outer, Inner, Last. It is a method for multiplying binomials.\n\nFirst means multiply the terms which occur first in each binomial, Outer means multiply the outermost terms in the product, Inner means multiply the innermost two terms, and Last means multiply the terms which occur last in each binomial.\n\nSo applying the FOIL method, \n\nFirst: \(9 * 9 = 81\), \n\nOuter: \(9 * -5x = -45x\), \n\nInner: \(-5x * 9 = -45x\), \n\nLast: \(-5x * -5x = 25x^2\).
04

Combine like terms

We should now combine the like terms to simplify the squared binomial. So, our equation becomes: \(81 + (-45x) + (-45x) + 25x^2\). When simplified, we're left with: \(25x^2 - 90x + 81\).

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