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Chapter 5: Problem 10

Remove the brackets from the given expression: \((x+1)(x-3)(x-1)\)

Short Answer

Expert verified
Question: Simplify the given expression: \((x+1)(x-3)(x-1)\) Answer: \(x^3 - 3x^2 - x + 3\)

Step by step solution

01

Expand the first two terms

First, expand the \((x+1)(x-3)\) part of the expression by applying the distributive property (FOIL method). Multiply the first terms, the outer terms, the inner terms, and the last terms, then add them up: \((x+1)(x-3) = (x \cdot x) + (-3 \cdot x) + (1 \cdot x) + (1 \cdot -3)\). This simplifies to \(x^2 - 2x - 3\).
02

Expand the result with the third term

Next, expand the result from Step 1 with the remaining term, \((x-1)\). Multiply each term from the result of Step 1 with each term from the \((x-1)\): \((x^2-2x-3)(x-1)\). Apply the distributive property (FOIL method) again: \((x^2-2x-3)(x-1) = (x^2 \cdot x) + (-1 \cdot x^2) + (-2x \cdot x) + (2x \cdot 1) + (-3 \cdot x) + (3 \cdot 1)\).
03

Combine like terms

Combine the like terms from the expression in Step 2: \(x^3 - x^2 - 2x^2 + 2x - 3x + 3 = x^3 - 3x^2 - x + 3\). This is the simplified form of the given expression after removing the brackets. So the final answer is: \(x^3 - 3x^2 - x + 3\).

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