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Chapter 5: Problem 72

Find each product. In each case, neither factor is a monomial. $$(2 a-3)\left(a^{2}-3 a+5\right)$$

Short Answer

Expert verified
The product of the two expressions (2a - 3) and \(a^{2} - 3a + 5\) is \(2a^{3}\) - 9\(a^{2}\) + 19a - 15

Step by step solution

01

Identify the expressions

We are given two algebraic expressions: (2a - 3) and \(a^{2} - 3a + 5\). We have to find their product.
02

Apply the distributive law

Apply the distributive property of multiplication over addition/subtraction to these two expressions. This means multiplying the term in the first expression by each term in the second expression and then summing up the results.
03

Multiply terms

Distribute and multiply each term in the first expression to each term in the second expression: 2a * \(a^{2}\) = \(2a^{3}\)2a * (-3a) = -6\(a^{2}\)2a * 5 = 10a-3 * \(a^{2}\) = -3\(a^{2}\)-3 * -3a = 9a-3 * 5 = -15
04

Combine like terms

Recombine the results to form a new expression: \(2a^{3}\) - 6\(a^{2}\) + 10a - 3\(a^{2}\)+ 9a - 15= \(2a^{3}\) - 9\(a^{2}\) + 19a - 15

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