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Chapter 5: Problem 63

Find each product. In each case, neither factor is a monomial. $$(2 x-5)(x+4)$$

Short Answer

Expert verified
So, the product of \( (2 x-5)(x+4) \) is \( 2x^2 + 3x - 20 \).

Step by step solution

01

Apply FOIL Method - First

The first step is to multiply the first terms of both binomials. That gives \(2x * x = 2x^2\).
02

Apply FOIL Method - Outer

Next, multiply the outer terms of the binomials, or the first term of the first binomial by the second term of the second binomial. That gives \(2x * 4 = 8x\).
03

Apply FOIL Method - Inner

Then, multiply the inner terms, or the second term of the first binomial by the first term of the second bilinear. That gives \(-5 * x = -5x\).
04

Apply FOIL Method - Last

Afterwards, multiply the last terms of both binomials. This gives \(-5 * 4 = -20\).
05

Add the Products

Finally, add all the obtained products, combining the like terms. The expression thus becomes \(2x^2 + 8x - 5x - 20 = 2x^2 + 3x - 20\).

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