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Chapter 5: Problem 9

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

Short Answer

Expert verified
Question: Remove the brackets from the expression \(x(x+1)(x-3)\). Answer: The expression with the brackets removed is \(x^3 - 2x^2 - 3x\).

Step by step solution

01

Multiply the two binomials

Let's first multiply the two binomials \((x+1)(x-3)\) using the distributive property (also known as the FOIL method). The distributive property states that \(a(b+c) = ab + ac\). In this case, let \(a = x\), \(b = x + 1\), and \(c = x - 3\). Using the distributive property to multiply the terms inside the brackets, we get: \((x+1)(x-3) = x(x-3) + 1(x-3)\) Now, distribute each term: \(x(x-3) = x^2 - 3x\) \(1(x-3) = x - 3\) Combine the two expressions: \(x^2 - 3x + x - 3\)
02

Simplify the expression

Now, we need to simplify the expression obtained in Step 1 by combining like terms. In this case, we have two x terms, which we can add together: \(-3x + x = (-3 + 1)x = -2x\) So our simplified expression is: \(x^2 - 2x - 3\)
03

Distribute x to the simplified expression

Finally, we need to distribute the x term outside the brackets: \(x(x^2 - 2x - 3)\) Using the distributive property, we get: \(x(x^2) - x(2x) - x(3)\) Which simplifies to: \(x^3 - 2x^2 - 3x\) So, the expression with the brackets removed is: \(\boxed{x^3 - 2x^2 - 3x}\)

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Most popular questions from this chapter

Show that (a) \(\frac{n !}{(n-1) !}=n\), (b) \(\frac{(n+1) !}{(n-1) !}=n(n+1)\) (c) \(\frac{n !}{(n+1) !}=\frac{1}{n+1}\).

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