1Cademy - Multiplying $$(2x + 7)(2x - 7)$$ Using the Product of Conjugates Pattern

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Multiplying $(2x + 5)(2x - 5)$ Using the Product of Conjugates Pattern

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Multiplying $(2x + 7)(2x - 7)$ Using the Product of Conjugates Pattern

Apply the Product of Conjugates Pattern to multiply $(2x + 7)(2x - 7)$ . Confirm the binomials are conjugates: both share the same first term $2x$ and the same last term $7$ , with one using addition and the other subtraction. Use the formula $(a + b)(a - b) = a^2 - b^2$ , where $a = 2x$ and $b = 7$ .

Step 1 — Square the first term, $2x$ : $(2x)^2 = 4x^2$ . Both the coefficient and the variable must be squared separately: $2^2 = 4$ and $x^2 = x^2$ . Step 2 — Square the last term, $7$ : $7^2 = 49$ . Step 3 — Write the difference of squares: $(2x + 7)(2x - 7) = 4x^2 - 49$

The product is $4x^2 - 49$ .

Updated 2026-04-29

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OpenStax Intermediate Algebra

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