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The problem asks to expand the expression $(x-2y)(x-7y)$.

AlgebraPolynomial ExpansionAlgebraic ManipulationDistributive Property
2025/4/27

1. Problem Description

The problem asks to expand the expression (x−2y)(x−7y)(x-2y)(x-7y).

2. Solution Steps

We will use the distributive property (also known as FOIL) to expand the expression:
(a+b)(c+d)=ac+ad+bc+bd(a+b)(c+d) = ac + ad + bc + bd
(x−2y)(x−7y)=x(x)+x(−7y)+(−2y)(x)+(−2y)(−7y)(x - 2y)(x - 7y) = x(x) + x(-7y) + (-2y)(x) + (-2y)(-7y)
=x2−7xy−2xy+14y2= x^2 - 7xy - 2xy + 14y^2
=x2−9xy+14y2= x^2 - 9xy + 14y^2

3. Final Answer

x2−9xy+14y2x^2 - 9xy + 14y^2

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