1Cademy - Solving $$(y - 8)^2 = 0$$ Using the Zero Product Property

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Quadratic Equation

Example

Solving $(y - 8)^2 = 0$ Using the Zero Product Property

Solve $(y - 8)^2 = 0$ by rewriting the squared binomial as a product and applying the Zero Product Property.

Step 1 — Rewrite the left side as a product. Because $(y - 8)^2$ means $(y - 8)$ multiplied by itself, rewrite the equation as:

$(y - 8)(y - 8) = 0$

Step 2 — Set each factor equal to zero using the Zero Product Property:

$y - 8 = 0 \quad \text{or} \quad y - 8 = 0$

Step 3 — Solve each equation. Both equations are identical:

$y = 8 \quad \text{and} \quad y = 8$

Because the solution repeats, $y = 8$ is a double root.

Step 4 — Check by substituting $y = 8$ into the original equation:

$(8 - 8)^2 = 0^2 = 0$ ✓

The solution is $y = 8$ . This example illustrates that when a quadratic equation takes the form of a squared binomial equal to zero, the two factors produced by expanding the square are identical, so the Zero Product Property yields only one distinct solution — a double root.

Updated 2026-04-21

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OpenStax Elementary Algebra

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