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

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Distributive Property

Example

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

Multiply $y(y - 2)$ , where the outside factor is a variable monomial rather than a numerical constant.

Step 1 — Distribute: Multiply $y$ by each term inside the parentheses:

$y \cdot y - y \cdot 2$

Step 2 — Simplify: For the first term, apply the Product Property for Exponents: $y \cdot y = y^{1+1} = y^2$ . For the second term, $y \cdot 2 = 2y$ :

$y^2 - 2y$

The result is $y^2 - 2y$ . When the monomial being distributed is itself a variable, the Product Property for Exponents comes into play — multiplying $y$ by $y$ produces $y^2$ , not $2y$ . This distinguishes distributing a variable monomial from distributing a numerical constant, where only arithmetic is needed.

Updated 2026-04-21

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OpenStax Elementary Algebra

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