Let us first find the HCF of all the terms of the given polynomial
3x2+6x2y+9xy2 by factoring the terms as follows:
3x2=3×x×x6x2y=3×2×x×x×y9xy2=3×3×x×y×y
Therefore, HCF=3×x=3x
Now, we factor out the HCF from each term of the polynomial 3x2+6x2y+9xy2 as shown below:
3x2+6x2y+9xy2=3x(x+2xy+3y2)
Hence, 3x2+6x2y+9xy2=3x(x+2xy+3y2).