1Cademy - Squaring $$(4x + 6)^2$$ Using the Binomial Squares Pattern

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Binomial Squares Pattern

Example

Squaring $(4x + 6)^2$ Using the Binomial Squares Pattern

Apply the Binomial Squares Pattern to multiply $(4x + 6)^2$ . Use the addition form $(a + b)^2 = a^2 + 2ab + b^2$ , where $a = 4x$ and $b = 6$ .

Step 1 — Square the first term: $(4x)^2 = 16x^2$ . Square the coefficient and the variable separately: $4^2 = 16$ and $x^2 = x^2$ .

Step 2 — Square the last term: $6^2 = 36$ .

Step 3 — Double their product: $2 \cdot (4x) \cdot 6 = 48x$ .

Assemble the three pieces into a trinomial:

$(4x + 6)^2 = 16x^2 + 48x + 36$

This example features a binomial whose first term is a monomial with a numerical coefficient greater than $1$ ( $4x$ ), while the second term is a plain constant ( $6$ ). A common mistake is writing $(4x)^2 = 4x^2$ instead of the correct $16x^2$ — when squaring a monomial like $4x$ , both the coefficient and the variable must be squared: $4^2 \cdot x^2 = 16x^2$ . This example bridges the gap between simple cases like $(x + 5)^2$ (where the variable has coefficient $1$ ) and more complex ones like $(2x - 3y)^2$ (where both terms involve variables with coefficients).

Updated 2026-04-21

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OpenStax Elementary Algebra

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