Answer:
Option (a) is correct.
The product of the given expression [tex]\left(y+3\right)\left(y^2-3y+9\right)[/tex] is [tex]y^3+27[/tex]
Step-by-step explanation:
Given : Expression [tex]\left(y+3\right)\left(y^2-3y+9\right)[/tex]
We have to find the product of the given expression [tex]\left(y+3\right)\left(y^2-3y+9\right)[/tex]
Consider the given expression [tex]\left(y+3\right)\left(y^2-3y+9\right)[/tex]
Apply distributive law,
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex], we have,
[tex]=yy^2+y\left(-3y\right)+y\cdot \:9+3y^2+3\left(-3y\right)+3\cdot \:9[/tex]
Simplify, we have,
[tex]=y^2y-3yy+9y+3y^2-3\cdot \:3y+3\cdot \:9[/tex]
Also,
[tex]=y^3-3y^2+9y+3y^2-9y+27[/tex]
Adding similar terms, we have,
[tex]=y^3+27[/tex]
Thus, The product of the given expression [tex]\left(y+3\right)\left(y^2-3y+9\right)[/tex] is [tex]y^3+27[/tex]
