The problem is to expand the product of two binomials: $(2x - 5y)(3x - 2y)$.

1. Problem Description

The problem is to expand the product of two binomials: $(2x - 5y)(3x - 2y)$.

2. Solution Steps

We use the distributive property (also known as the FOIL method) to expand the product:

$(a + b)(c + d) = ac + ad + bc + bd$

Applying this to our problem:

$(2x - 5y)(3x - 2y) = (2x)(3x) + (2x)(-2y) + (-5y)(3x) + (-5y)(-2y)$

Now, we perform each multiplication:

$(2x)(3x) = 6x^2$

$(2x)(-2y) = -4xy$

$(-5y)(3x) = -15xy$

$(-5y)(-2y) = 10y^2$

So we have:

$6x^2 - 4xy - 15xy + 10y^2$

Combine the like terms $-4xy$ and $-15xy$:

$-4xy - 15xy = -19xy$

Therefore, the expression simplifies to:

$6x^2 - 19xy + 10y^2$

3. Final Answer

$6x^2 - 19xy + 10y^2$