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Chapter 5: Problem 41

Find each product. $$(x-3 y)(2 x+7 y)$$

Short Answer

Expert verified
The product of the given expression, \((x - 3y)(2x + 7y)\), is \(2x^2 + 7xy - 6xy - 21y^2\), which simplifies to \(2x^2 + xy - 21y^2\).

Step by step solution

01

Distributive Property

Multiply each term in the first binomial, \(x - 3y\), by each term in the second binomial, \(2x + 7y\). Begin by multiplying \(x\) by \(2x\) and \(x\) by \(7y\).
02

Continue with Distributive Property

Continue by multiplying \(-3y\) by \(2x\) and then \(-3y\) by \(7y\). This completes the multiplication of each term from the first binomial by each term in the second binomial.
03

Simplification

Combine like terms, if any, to simplify the expression.

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Most popular questions from this chapter

In Exercises \(85-86,\) the variable \(n\) in each exponent represents a natural Number. Divide the polynomial by the monomial. Then use polynomial multiplication to check the quotient. $$\frac{12 x^{15 n}-24 x^{12 n}+8 x^{3 n}}{4 x^{3 n}}$$

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