/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 35 Find each product. $$ (9 y-2... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 35

Find each product. $$ (9 y-2)\left(8 y^{2}-6 y+1\right) $$

Short Answer

Expert verified
The product is \(72y^3 - 70y^2 + 21y - 2\).

Step by step solution

01

- Distribute the First Term

Distribute the first term of the first polynomial, which is \(9y\), to each term of the second polynomial \((8y^2 - 6y + 1)\). This gives us three terms: \ \(9y \times 8y^2\), \(9y \times -6y\), and \(9y \times 1\).
02

- Calculate the Products from Step 1

Calculate the products: \ \(9y \times 8y^2 = 72y^3\), \ \(9y \times -6y = -54y^2\), \ \(9y \times 1 = 9y\).
03

- Distribute the Second Term

Next, distribute the second term of the first polynomial, which is \(-2\), to each term of the second polynomial \((8y^2 - 6y + 1)\). This gives us three more terms: \ \(-2 \times 8y^2\), \(-2 \times -6y\), and \(-2 \times 1\).
04

- Calculate the Products from Step 3

Calculate the products: \ \(-2 \times 8y^2 = -16y^2\), \ \(-2 \times -6y = 12y\), \ \(-2 \times 1 = -2\).
05

- Combine Like Terms

Combine all the terms from steps 2 and 4 and then combine the like terms: \ \(72y^3 - 54y^2 + 9y - 16y^2 + 12y - 2\). \ Combine like terms to get: \ \(72y^3 + (-54y^2 - 16y^2) + (9y + 12y) - 2\) \ which simplifies to: \ \(72y^3 - 70y^2 + 21y - 2\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distributive Property
The Distributive Property is a fundamental aspect of algebra. It allows us to distribute, or
Polynomial Products
Polynomial Products involve multiplying one polynomial by another. Each term in the first polynomial

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