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Chapter 5: Problem 67

Find each product. $$(x-y)\left(x^{2}-3 x y+y^{2}\right)$$

Short Answer

Expert verified
The product is \(x^{3} - 4x^{2}y + 4xy^{2} - y^{3}\)

Step by step solution

01

Distribute (x-y)

Multiply each term from the polynomial \(x^{2}-3 x y+y^{2}\) by the terms in the binomial (x-y). This gives us: \(x(x^{2}-3 x y+y^{2}) - y(x^{2}-3 x y+y^{2})\)
02

Simplify

Simplify by multiplying each term: \(x^{3} - 3x^{2}y + xy^{2} - x^{2}y + 3xy^{2} - y^{3}\)
03

Combine like terms

Combine the like terms: \(x^{3} - 4x^{2}y + 4xy^{2} - y^{3}\)

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Most popular questions from this chapter

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Other than multiplying monomials, the distributive property is used to multiply other kinds of polynomials.

Perform the indicated operations. $$(x+5)(x-6)-(x+2)(x-9)$$

In Exercises \(105-106,\) find the missing coefficients and exponents designated by question marks. $$\frac{3 x^{14}-6 x^{12}-7 x^{7}}{2 x^{7}}=-x^{7}+2 x^{5}+3$$

Will help you prepare for the material covered in the next section. In each exercise, find the indicated products. Then, if possible, state a fast method for finding these products. (You may already be familiar with some of these methods from a high school algebra course.) a. \((x+3)^{2}\) b. \((x+5)^{2}\)

Perform the indicated operations. $$(y+1)\left(y^{2}-y+1\right)+(y-1)\left(y^{2}+y+1\right)$$
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