1Cademy - Multiplying $$(3x - y)(3x + y)$$ Using the Product of Conjugates Pattern

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Multiplying $(5m - 9n)(5m + 9n)$ Using the Product of Conjugates Pattern

Example

Multiplying $(3x - y)(3x + y)$ Using the Product of Conjugates Pattern

Apply the Product of Conjugates Pattern to multiply $(3x - y)(3x + y)$ . Both binomials share the same first term $3x$ and the same last term $y$ , with one using subtraction and the other addition, confirming they are conjugates. Use the formula $(a - b)(a + b) = a^2 - b^2$ , where $a = 3x$ and $b = y$ .

Step 1 — Square the first term, $3x$ : $(3x)^2 = 9x^2$ . Square the coefficient and the variable separately: $3^2 = 9$ and $x^2 = x^2$ . Step 2 — Square the last term, $y$ : $y^2 = y^2$ . Step 3 — Write the difference of squares: $(3x - y)(3x + y) = 9x^2 - y^2$

The product is $9x^2 - y^2$ .

Updated 2026-04-29

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OpenStax Intermediate Algebra

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