1Cademy - Multiplying $$(3y - 1)(2y - 6)$$ Using the Vertical Method

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The Vertical Method for Multiplying Binomials

Example

Multiplying $(3y - 1)(2y - 6)$ Using the Vertical Method

Multiply $(3y - 1)(2y - 6)$ using the Vertical Method — the process mirrors multi-digit whole-number multiplication, with partial products aligned by like terms.

Step 1 — Set up vertically: Write one binomial above the other (it does not matter which goes on top):

$3y - 1$ $\times \quad 2y - 6$

Step 2 — Multiply the top binomial by $-6$ : Multiply each term of $3y - 1$ by $-6$ :

$(-6)(3y) = -18y$ and $(-6)(-1) = 6$

Write the first partial product: $-18y + 6$ .

Step 3 — Multiply the top binomial by $2y$ : Multiply each term of $3y - 1$ by $2y$ :

$(2y)(3y) = 6y^2$ and $(2y)(-1) = -2y$

Write the second partial product: $6y^2 - 2y$ , aligning like terms beneath the first partial product.

Step 4 — Add the partial products: Combine like terms column by column. The $y^2$ column has $6y^2$ . The $y$ column has $-18y + (-2y) = -20y$ . The constant column has $6$ :

$6y^2 - 20y + 6$

The result is $6y^2 - 20y + 6$ . The partial products $-18y + 6$ and $6y^2 - 2y$ are exactly the same four terms produced by the FOIL method, just arranged vertically with like terms aligned in columns instead of written in a single row.

Updated 2026-04-21

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OpenStax Elementary Algebra

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