The completely factored form is 0.09y^2−0.81=0.09(y+3)(y−3).
To factor the expression 0.09y^2 −0.81, let's first factor out the common factor, which is 0.09.
0.09y^2 −0.81=0.09(y^2 −9)
Now, observe that y^2 −9 is a difference of squares, which can be factored further.
The difference of squares formula is
a^2 −b^2 =(a+b)(a−b). In this case,
a=y and b=3.
y^2 −9=(y+3)(y−3)
So, the completely factored form is 0.09y^2−0.81=0.09(y+3)(y−3).