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Chapter 0: Problem 22

Find each product. $$(x-1)(x+2)$$

Short Answer

Expert verified
The product of \( (x - 1)(x + 2) \) is \( x^2 + x - 2 \).

Step by step solution

01

Applying Distributive Property

Use the distributive property to distribute each term in the first parenthesis, \( (x - 1) \), to each term in the second parenthesis, \( (x + 2) \). This gives four terms in total: \(x \times x\), \(x \times 2\), \(-1 \times x\), and \(-1 \times 2\).
02

Performing Multiplications

Multiply each pair of terms from the previous step: \(x \times x\) gives \(x^2\), \(x \times 2\) gives \(2x\), \(-1 \times x\) gives \(-x\), and \(-1 \times 2\) gives \(-2\). This results in the expression \(x^2 + 2x - x - 2\).
03

Simplifying the Expression

Combine like terms to simplify the expression. The terms \(2x\) and \(-x\) are similar, thus can be combined into a single term. This results in the final simplified expression \(x^2 + x - 2\).

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