To find the product of [tex]\(\left(5 y^2-6 y\right)\left(7 y^7-y^3\right)\)[/tex], we will use the distributive property (also known as the FOIL method for binomials). We can break it down into steps:
1. First Term from the First Expression, Multiplied by Each Term in the Second Expression:
[tex]\[
(5y^2) \cdot (7y^7) = 35y^9
\][/tex]
[tex]\[
(5y^2) \cdot (-y^3) = -5y^5
\][/tex]
2. Second Term from the First Expression, Multiplied by Each Term in the Second Expression:
[tex]\[
(-6y) \cdot (7y^7) = -42y^8
\][/tex]
[tex]\[
(-6y) \cdot (-y^3) = 6y^4
\][/tex]
3. Combining All These Products:
[tex]\[
35y^9 - 5y^5 - 42y^8 + 6y^4
\][/tex]
4. Writing in Descending Order of Exponents:
[tex]\[
35y^9 - 42y^8 - 5y^5 + 6y^4
\][/tex]
Therefore, the product of [tex]\(\left(5 y^2-6 y\right)\left(7 y^7-y^3\right)\)[/tex] in descending order of exponents is:
[tex]\[
35y^9 - 42y^8 - 5y^5 + 6y^4
\][/tex]
