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Chapter 5: Problem 93

Perform the indicated operations. $$(x+4)(x-5)-(x+3)(x-6)$$

Short Answer

Expert verified
The solution to \((x+4)(x-5)-(x+3)(x-6)\) is \(2x - 2\).

Step by step solution

01

Distribute the Values in the First Parentheses

Using the FOIL method, expand the first expression \((x+4)(x-5)\) to obtain \(x^2+4x-5x-20\) which simplifies to \(x^2-x-20\).
02

Distribute Values in the Second Parentheses

Again, apply the FOIL method to expand the second expression \((x+3)(x-6)\) to get \(x^2+3x-6x-18\) which simplifies to \(x^2-3x-18\).
03

Subtract Second Result from First

Subtract the expanded second expression from the first to find the final solution. Be cautious with signs: \(x^2-x-20 - (x^2-3x-18) = x^2-x-20 -x^2+3x+18\).
04

Simplify the Expression

Combine like terms to simplify the expression further: \(2x - 2\).

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Most popular questions from this chapter

In each exercise, find the product. $$(x+3)\left(x^{2}+5\right)$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. It is not possible to write a binomial with degree \(0 .\)

Express \(\frac{7}{8}\) as a decimal. (Section \(1.3,\) Example 4 )

Find the slope of the line passing through the points \((-2,8)\) and \((1,6) .\) (Section 3.3, Example 1)

Will help you prepare for the material covered in the next section. In each exercise, find the indicated products. Then, if possible, state a fast method for finding these products. (You may already be familiar with some of these methods from a high school algebra course.) a. \((x+3)^{2}\) b. \((x+5)^{2}\)
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