Problem 26 - College Algebra Essentials

Question

Find each product. $$(2 x-5)(7 x+2)$$

Step-by-Step Solution

Answer

The product of the two binomials \((2x - 5)(7x + 2)\) is \(14x^2 - 31x - 10.\)

Step 1: Identify the Terms of the Binomials

The terms of the first binomial, \(2x - 5\), are \(2x\) and \(-5\). Similarly, the terms of the second binomial, \(7x + 2\), are \(7x\) and \(2\).

Step 2: Apply the FOIL Method

The FOIL method stands for First, Outer, Inner, and Last. It is used to multiply each term in the first binomial by each term in the second binomial. So, \((2x - 5) (7x + 2)\) equals \((2x * 7x) + (2x * 2) + (-5 * 7x) + (-5 * 2)\).

Step 3: Simplify the Expression

To simplify the expression, you follow the order of operations, which is to multiply before adding or subtracting. Thus, you get \(14x^2 + 4x - 35x - 10\). This can be further simplified to \(14x^2 - 31x - 10\).