1Cademy - Squaring $$(x + 5)^2$$ Using the Binomial Squares Pattern

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Binomial Squares Pattern

Example

Squaring $(x + 5)^2$ Using the Binomial Squares Pattern

Apply the Binomial Squares Pattern to multiply $(x + 5)^2$ . Here $a = x$ and $b = 5$ , so use the formula $(a + b)^2 = a^2 + 2ab + b^2$ .

Step 1 — Square the first term: $x^2$ .

Step 2 — Square the last term: $5^2 = 25$ .

Step 3 — Double their product: $2 \cdot x \cdot 5 = 10x$ .

Assemble the three pieces into a trinomial:

$(x + 5)^2 = x^2 + 10x + 25$

This example demonstrates the simplest application of the pattern: both terms of the binomial have a coefficient of $1$ (or are a plain constant), and the binomial uses addition, so all three terms in the resulting trinomial are positive.

Updated 2026-04-21

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OpenStax Elementary Algebra
OpenStax Elementary Algebra

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