Question

using tiles to multiply a monomial by a binomial

multiply \\(3x(2x - 1)\\) by following these steps:

step 1: drag tiles to the section labeled factor 1 to represent the factor \\(3x\\).
step 2: drag tiles to the section labeled factor 2 to represent the factor \\(2x - 1\\).

Explanation:

Represent Factor 1

$$ \text{Factor 1} = 3x \implies \text{Three } +x \text{ tiles placed horizontally at the top.} $$

Represent Factor 2

$$ \text{Factor 2} = 2x - 1 \implies \text{Two } +x \text{ tiles and one } -1 \text{ tile placed vertically along the left side.} $$

Determine the Product

$$ 3x(2x - 1) = 3x(2x) + 3x(-1) = 6x^2 - 3x $$

Answer:

To multiply \(3x(2x - 1)\) using algebra tiles:

1. Factor 1 (top row): Place three \(+x\) tiles horizontally.
2. Factor 2 (left column): Place two \(+x\) tiles and one \(-1\) tile vertically.
3. Product area: Fill in the grid by multiplying the intersecting tiles:

• Six \(x^2\) tiles (from \(3x \times 2x\))
• Three \(-x\) tiles (from \(3x \times -1\))

The simplified product is:

$$6x^2 - 3x$$