Factor \( 16 x^{2}-56 x y+49 y^{2} \)

The given expression is: \[ 16x^{2} - 56xy + 49y^{2} \] To factor this quadratic expression, let's check if it is a perfect square trinomial. A perfect square trinomial has the form: \[ (ax + by)^2 = a^2x^2 + 2abxy + b^2y^2 \] Let's compare this with the given expression: 1. **First Term (\(a^2x^2\))**: \(16x^2\) can be written as \((4x)^2\), so \(a = 4\). 2. **Last Term (\(b^2y^2\))**: \(49y^2\) can be written as \((7y)^2\), so \(b = 7\). 3. **Middle Term (\(2abxy\))**: Substituting \(a = 4\) and \(b = 7\) into \(2abxy\) gives: \(2 \times 4 \times 7 \times xy = 56xy\). However, the given middle term is \(-56xy\), which indicates that the binomial should have a negative sign. Putting it all together: \[ 16x^{2} - 56xy + 49y^{2} = (4x - 7y)^2 \] **Final Factored Form:** \[ (4x - 7y)^2 \]