1-18y+81y2

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!