81b 2 −90b+25 .

To simplify the expression \( 81b^2 - 90b + 25 \), we can check if it can be factored or if we need to use the quadratic formula to find the roots.

First, let's see if we can factor the quadratic expression.

The expression is of the form \( ax^2 + bx + c \), where:

• \( a = 81 \)
• \( b = -90 \)
• \( c = 25 \)

To see if it can be factored, we look for two numbers that multiply to \( ac = 81 \cdot 25 = 2025 \) and add to \( -90 \).

The factors of \( 2025 \) that sum up to \( -90 \) are \( -45 \) and \( -45 \). This means we can factor the expression as:

\[ 81b^2 - 90b + 25 = (9b - 5)(9b - 5) \]

or

\[ (9b - 5)^2 \]

Therefore, the factorized form of the expression \( 81b^2 - 90b + 25 \) is \((9b - 5)^2\).

If you need any further assistance, feel free to ask!