Sure, let's solve the expression [tex]\((2x - 3y)(-xy + 6x - 3y)\)[/tex] step by step by expanding it.
Step 1: Distribute each term in the first parenthesis to each term in the second parenthesis.
First, we distribute [tex]\(2x\)[/tex]:
[tex]\[ 2x \cdot (-xy) = -2x^2y \][/tex]
[tex]\[ 2x \cdot 6x = 12x^2 \][/tex]
[tex]\[ 2x \cdot (-3y) = -6xy \][/tex]
Next, we distribute [tex]\(-3y\)[/tex]:
[tex]\[ -3y \cdot (-xy) = 3xy^2 \][/tex]
[tex]\[ -3y \cdot 6x = -18xy \][/tex]
[tex]\[ -3y \cdot (-3y) = 9y^2 \][/tex]
Step 2: Combine all the distributed terms:
[tex]\[ -2x^2y + 12x^2 - 6xy + 3xy^2 - 18xy + 9y^2 \][/tex]
Step 3: Combine like terms:
[tex]\[ -2x^2y + 12x^2 - 6xy - 18xy + 3xy^2 + 9y^2 \][/tex]
[tex]\[ -2x^2y + 12x^2 - 24xy + 3xy^2 + 9y^2 \][/tex]
So, the expanded form of the expression [tex]\((2x - 3y)(-xy + 6x - 3y)\)[/tex] is:
[tex]\[ -2x^2y + 12x^2 + 3xy^2 - 24xy + 9y^2 \][/tex]
This is the final answer.
