\( 1 \leftarrow \quad \) Multiply the following binomials. \[ (4 x-7 y)(7 x-y) \]

To multiply the binomials \( (4x - 7y)(7x - y) \), we can use the distributive property, also known as the FOIL method for binomials. First, multiply the first terms: \( 4x \cdot 7x = 28x^2 \). Next, multiply the outer terms: \( 4x \cdot (-y) = -4xy \). Then, the inner terms: \( -7y \cdot 7x = -49xy \). Lastly, the last terms: \( -7y \cdot (-y) = 7y^2 \). Combining all these gives us: \[ 28x^2 - 4xy - 49xy + 7y^2 = 28x^2 - 53xy + 7y^2. \] So the result is \( 28x^2 - 53xy + 7y^2 \). Alternatively, you could think of this as a way of combining like terms where you end up with a new polynomial that reflects the interaction between the two expressions! Mathematics is all about making connections, after all!