To simplify the expression ( 1 - 18y + 81y^2 ), we can rearrange the terms:
[ 81y^2 - 18y + 1 ]
This expression is a quadratic in the standard form ( ay^2 + by + c ), where ( a = 81 ), ( b = -18 ), and ( c = 1 ).
If you're looking to factor this expression, we'll check if it can be expressed in a factored form. The quadratic can potentially be factored as:
[ (py + q)(ry + s) ]
To factor ( 81y^2 - 18y + 1 ), we need two numbers that multiply to ( a \cdot c = 81 \cdot 1 = 81 ) and add up to ( b = -18 ). The numbers that meet these criteria are ( -9 ) and ( -9 ).
Thus, we can rewrite the quadratic as:
[ 81y^2 - 9y - 9y + 1 ]
Grouping the terms gives:
[ (81y^2 - 9y) - (9y - 1) ]
Factoring by grouping:
[ 9y(9y - 1) - 1(9y - 1) ]
This simplifies to:
[ (9y - 1)(9y - 1) \text{ or } (9y - 1)^2 ]
So, the factored form of the expression ( 1 - 18y + 81y^2 ) is:
[
(9y - 1)^2
]
If you need further assistance or specific information about this expression, just let me know!
