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Chapter 0: Problem 69

Find each product. $$(x-y)\left(x^{2}+x y+y^{2}\right)$$

Short Answer

Expert verified
The answer is \( x^{3}+x^{2}y+x y^{2} -yx^{2} -y^{2}x - y^{3} \)

Step by step solution

01

Multiply using the distributive property

Begin by multiplying each term in the first expression by each term in the second expression. So, \( (x) \times (x^{2}+x y+y^{2}) \) and then \( (-y) \times (x^{2}+x y+y^{2}) \)
02

Break down the multiplication

Break down the multiplication further as such: \( x \times x^{2} \), \( x \times xy \) and \( x \times y^{2} \) for the first multiplication, and then \( -y \times x^{2} \), \( -y \times xy \) and \( -y \times y^{2} \) for the second multiplication.
03

Perform the multiplications

Perform the multiplication for each term as such: \( x \times x^{2}=x^{3} \), \( x \times xy=x^{2}y \) and \( x \times y^{2}=x y^{2} \) for the first multiplication, and then \( -y \times x^{2}=-yx^{2} \), \( -y \times xy=-y^{2}x \) and \( -y \times y^{2}=-y^{3} \) for the second multiplication.
04

Combine like terms

Now you have \( x^{3}+x^{2}y+x y^{2} -yx^{2} -y^{2}x -y^{3} \). Combine like terms to get the final answer.

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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: $$ 2 x^{4}\left(8 x^{4}+3 x\right) $$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \(a x^{2}+c=0, a \neq 0,\) cannot be solved by the quadratic formula.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I evaluated \(\frac{3 x-3}{4 x(x-1)}\) for \(x=1\) and obtained 0.

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Describe the solution set of \(|x|>-4\)
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