Example

Multiplying (6x+5)(6x5)(6x + 5)(6x - 5) Using the Product of Conjugates Pattern

Apply the Product of Conjugates Pattern to multiply (6x+5)(6x5)(6x + 5)(6x - 5). Confirm the binomials are conjugates: both share the same first term 6x6x and the same last term 55, with one using addition and the other subtraction. Use the formula (a+b)(ab)=a2b2(a + b)(a - b) = a^2 - b^2, where a=6xa = 6x and b=5b = 5.

Step 1 — Square the first term, 6x6x: (6x)2=36x2(6x)^2 = 36x^2. Both the coefficient and the variable must be squared separately: 62=366^2 = 36 and x2=x2x^2 = x^2. Step 2 — Square the last term, 55: 52=255^2 = 25. Step 3 — Write the difference of squares: (6x+5)(6x5)=36x225(6x + 5)(6x - 5) = 36x^2 - 25

The product is 36x22536x^2 - 25.

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Updated 2026-04-29

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