Question

using a table to multiply multivariable polynomials

drag each tile to the table to multiply \\((6x - y)(2x - y + 2)\\).

tiles:
\\(y^2\\), \\(12x\\), \\(-6xy\\), \\(12x^2\\), \\(-2y\\), \\(-2xy\\)

table:

	\\(2x\\)	\\(-y\\)	\\(2\\)
\\(-y\\)

Explanation:

Set up the multiplication table

The rows represent the terms of the first polynomial:
Row 1: \(6x\)
Row 2: \(-y\)

The columns represent the terms of the second polynomial:
Column 1: \(2x\)
Column 2: \(-y\)
Column 3: \(2\)

Calculate the product for each cell

Row 1, Column 1: \((6x) \cdot (2x) = 12x^2\)
Row 1, Column 2: \((6x) \cdot (-y) = -6xy\)
Row 1, Column 3: \((6x) \cdot (2) = 12x\)
Row 2, Column 1: \((-y) \cdot (2x) = -2xy\)
Row 2, Column 2: \((-y) \cdot (-y) = y^2\)
Row 2, Column 3: \((-y) \cdot (2) = -2y\)

Match products to the table cells

Row 1:

• Cell 1: \(12x^2\)
• Cell 2: \(-6xy\)
• Cell 3: \(12x\)

Row 2:

• Cell 1: \(-2xy\)
• Cell 2: \(y^2\)
• Cell 3: \(-2y\)

Answer:

	\(2x\)	\(-y\)	\(2\)
\(-y\)	\(-2xy\)	\(y^2\)	\(-2y\)