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