Respuesta :
Answer: [tex]2x^7 -16a^6 +18a^5[/tex]
Step-by-step explanation: Given expression [tex](a^2)(2a^3)(a^2-8a + 9)[/tex].
The first factor [tex](a^2)[/tex] has a degree of : 2 because power of a is 2.
The second factor [tex](2a^3)[/tex] has a degree of : 3 because power of a is 3.
The third factor [tex](a^2-8a + 9)[/tex] has a degree of : 2 because highest power of a is 2.
Let us multiply them now:
[tex](a^2)(2a^3)(a^2-8a + 9).[/tex]
First we would multiply [tex](a^2)(2a^3)[/tex].
According to product rule of exponents, we would add the powers of a.
Therefore,
[tex](a^2)(2a^3) = 2a^{2+3}= 2a^5[/tex]
Now, we need to distribute [tex]2a^5[/tex] over [tex](a^2-8a + 9)[/tex]
Therefore,
[tex](2a^5)(a^2-8a + 9)= 2a^{5+2} -16a^{5+1}+18a^5[/tex]
=[tex]2x^7 -16a^6 +18a^5[/tex]
Highest power of resulting polynomial [tex]2x^7 -16a^6 +18a^5[/tex] is 7.
Therefore, The product has a degree of 7.
