1Cademy - Multiplying $$(x - 2)(x - y)$$ Using the Distributive Property

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Multiplying a Binomial by a Binomial Using the Distributive Property

Example

Multiplying $(x - 2)(x - y)$ Using the Distributive Property

Multiply $(x - 2)(x - y)$ by applying the Distributive Property twice — this product involves two different variables, $x$ and $y$ , which means the expanded result may contain no like terms.

Step 1 — Distribute $(x - y)$ to each term of the first binomial: Treat $(x - y)$ as a single unit and distribute it to $x$ and $-2$ :

$x(x - y) - 2(x - y)$

Step 2 — Distribute again within each product: For the first part: $x \cdot x = x^2$ and $x \cdot (-y) = -xy$ . For the second part: $-2 \cdot x = -2x$ and $-2 \cdot (-y) = 2y$ :

$x^2 - xy - 2x + 2y$

Step 3 — Check for like terms: The four terms are $x^2$ , $-xy$ , $-2x$ , and $2y$ . Each has a different variable structure, so there are no like terms to combine.

The result is $x^2 - xy - 2x + 2y$ . When two binomials contain different variables, the four products from the double distribution often have no like terms, leaving the expanded polynomial with four terms rather than the three-term trinomial that typically results from multiplying single-variable binomials.

Updated 2026-04-21

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OpenStax Elementary Algebra

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