 # To find: the product of two polynomials (8y-7) and (2y^{2}+7y-3) using indicated operation. Josalynn 2021-08-02 Answered
To find:
The product of two polynomials $\left(8y-7\right)$ and $\left(2{y}^{2}+7y-3\right)$ using indicated operation.
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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 $\left(8y-7\right)\left(2{y}^{2}+7y-3\right)$
To find the product of two polynomials $\left(8y-7\right)$ and $\left(2{y}^{2}+7y-3\right)$, is to distribute each term of $\left(8y-7\right)$, multiplying by each term of $\left(2{y}^{2}+7y-3\right)$
$=8y\left(2{y}^{2}+7y-3\right)-7\left(2{y}^{2}+7y-3\right)$
$=16{y}^{3}+56{y}^{2}-24y-14{y}^{2}-49y+21$ [Distributive law]
$=16{y}^{3}+\left(56{y}^{2}-14{y}^{2}\right)+\left(-24y-49y\right)+21$ [Grouping like terms]
$=16{y}^{3}+42{y}^{2}-73y+21$ [adding coefficients of like terms]
Final statement:
Therefore, $\left(8y-7\right)\left(2{y}^{2}+7y-3\right)=16{y}^{3}+42{y}^{2}-73y+21$
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