Question

multiply.
(4x - 5y)(4x + 7y)
simplify your answer.

Explanation:

Step1: Apply the distributive property (FOIL method)

Multiply the First terms: \(4x \times 4x = 16x^2\)
Multiply the Outer terms: \(4x \times 7y = 28xy\)
Multiply the Inner terms: \(-5y \times 4x = -20xy\)
Multiply the Last terms: \(-5y \times 7y = -35y^2\)
So we have \(16x^2 + 28xy - 20xy - 35y^2\)

Step2: Combine like terms

Combine the \(xy\) terms: \(28xy - 20xy = 8xy\)
So the simplified expression is \(16x^2 + 8xy - 35y^2\)

Answer:

\(16x^2 + 8xy - 35y^2\)