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Chapter 0: Problem 55

Find each product. $$(x-3)^{3}$$

Short Answer

Expert verified
The result of expanding \( (x-3)^{3} \) is \( x^3 - 9x^2 + 27x - 27 \).

Step by step solution

01

Write the Original Expression

Start with the original expression \( (x-3)^{3} \). This basically means \( (x-3) * (x-3) * (x-3) \).
02

Multiply the first two binomials

Apply the distributive law (FOIL) to \( (x-3)^{2} = (x-3)*(x-3) \). This will give \( x^2 - 6x +9 \). It is important to remember that \( (a-b)^2 = a^2 - 2ab + b^2 \).
03

Multiply the result by the third binomial

Now, multiply the result from Step 2 by the third binomial \( (x-3) \), which gives \( (x^2 - 6x + 9)*(x-3) \). After performing the multiplication, it gives \( x^3 - 9x^2 + 27x - 27 \).

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Most popular questions from this chapter

Exercises \(142-144\) will help you prepare for the material covered in the next section. Use the distributive property to multiply: $$ 2 x^{4}\left(8 x^{4}+3 x\right) $$

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