Ask AI: 16b²-40b+25 factor

To factor the quadratic expression \(16b^2 - 40b + 25\), let's follow these steps: 1. **Identify the coefficients**: The quadratic expression is in the form \(ax^2 + bx + c\), where: - \(a = 16\) - \(b = -40\) - \(c = 25\) 2. **Check for a perfect square trinomial**: A perfect square trinomial is expressed as \((dx + e)^2\), where \(d^2 = a\) and \(e^2 = c\). 3. **Determine the perfect squares**: - \(16b^2\) can be written as \((4b)^2\) - \(25\) can be written as \(5^2\) 4. **Check the middle term**: - For the middle term to fit, it should match the value \(2 \cdot d \cdot e\): \[2 \cdot 4b \cdot 5 = 40b\] - Since our middle term is \(-40b\), it should be \(2 \cdot 4b \cdot (-5)\). So, our expression fits the pattern of a perfect square trinomial, where: \[16b^2 - 40b + 25 = (4b - 5)^2\] Thus, the factored form of \(16b^2 - 40b + 25\) is: \[(4b - 5)^2\]