Problem 79 - Algebra 1: Concepts and Skills

Question

Find the product. $$(2 x-3)(5 x-9)$$

Step-by-Step Solution

Answer

The product of \((2x - 3)\) and \((5x - 9)\) is \(10x^2 -33x + 27\).

Step 1: Identify the terms in each binomial

The first binomial is \(2x - 3\) and the second binomial is \(5x - 9\). Here, \(2x\) and \(-3\) are terms of the first binomial, whereas \(5x\) and \(-9\) are the terms of the second binomial.

Step 2: Apply the FOIL Method

To do this, we Multiply the First terms in each binomial, then the Outer terms, then the Inner terms, and finally the Last terms. Following this order: \((2x)(5x) = 10x^2\), \((2x)(-9) = -18x\), \((-3)(5x) = -15x\), and \((-3)(-9) = 27\).

Step 3: Combine like terms

By combining the middle terms, those multiplied by x, we get: \(10x^2 -18x -15x + 27 = 10x^2 -33x + 27\).