To find:

The product of two polynomials$(8y-7)$ and $(2{y}^{2}+7y-3)$ using indicated operation.

The product of two polynomials

Josalynn
2021-08-02
Answered

To find:

The product of two polynomials$(8y-7)$ and $(2{y}^{2}+7y-3)$ using indicated operation.

The product of two polynomials

You can still ask an expert for help

Benedict

Answered 2021-08-03
Author has **108** answers

Concept:

Multiplication of polynomials:

1) To find the product of two polynomials, distribute each term of one polynomial, multiplying by each term of other polynomial.

2) Another method is to write such a product vertically, similar to the method used in arithmetic for multiplying whole numbers.

Calculation:

Given that$(8y-7)(2{y}^{2}+7y-3)$

To find the product of two polynomials$(8y-7)$ and $(2{y}^{2}+7y-3)$ , is to distribute each term of $(8y-7)$ , multiplying by each term of $(2{y}^{2}+7y-3)$

$=8y(2{y}^{2}+7y-3)-7(2{y}^{2}+7y-3)$

$=16{y}^{3}+56{y}^{2}-24y-14{y}^{2}-49y+21$ [Distributive law]

$=16{y}^{3}+(56{y}^{2}-14{y}^{2})+(-24y-49y)+21$ [Grouping like terms]

$=16{y}^{3}+42{y}^{2}-73y+21$ [adding coefficients of like terms]

Final statement:

Therefore,$(8y-7)(2{y}^{2}+7y-3)=16{y}^{3}+42{y}^{2}-73y+21$

Multiplication of polynomials:

1) To find the product of two polynomials, distribute each term of one polynomial, multiplying by each term of other polynomial.

2) Another method is to write such a product vertically, similar to the method used in arithmetic for multiplying whole numbers.

Calculation:

Given that

To find the product of two polynomials

Final statement:

Therefore,

Jeffrey Jordon

Answered 2022-07-06
Author has **2262** answers

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