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Chapter 5: Problem 34

Find each product. $$6 x^{2} y\left(5 x^{2}-9 y\right)$$

Short Answer

Expert verified
The product of the given expression is \(30x^4y - 54x^2y^2\).

Step by step solution

01

Identification of terms

Identify the monomial and the terms of the binomial in the given expression. In this case, the monomial is \(6x^2y\) and the binomial consists of terms \(5x^2\) and \(-9y\).
02

Apply Distributive Law - Part 1

Multiply the monomial \(6x^2y\) with the first term of the binomial \(5x^2\). The product is \(30x^4y\) (because when you multiply variables with the same base, you add the exponents and 5*6=30).
03

Apply Distributive Law - Part 2

Multiply the monomial \(6x^2y\) with the second term of the binomial \(-9y\). The product is \(-54x^2y^2\) (because when you multiply variables with the same base, you add the exponents and -9*6=-54).
04

Combine the results

Combine the products from Step 2 and Step 3 to form a single expression. Therefore, \(6x^2y(5x^2 - 9y) = 30x^4y - 54x^2y^2\).

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