Example

Multiplying (5y+2)(6y3)(5y + 2)(6y - 3) Using the Distributive Property

Multiply (5y+2)(6y3)(5y + 2)(6y - 3) by applying the Distributive Property twice. Begin by distributing the entire second binomial, (6y3)(6y - 3), to each term in the first binomial: 5y(6y3)+2(6y3)5y(6y - 3) + 2(6y - 3). Then, expand each part by distributing again: multiply 5y5y into (6y3)(6y - 3) to get 30y215y30y^2 - 15y, and multiply 22 into (6y3)(6y - 3) to get 12y612y - 6. The full expression is now 30y215y+12y630y^2 - 15y + 12y - 6. Combine the like middle terms, 15y-15y and 12y12y, to simplify the expression into the final trinomial: 30y23y630y^2 - 3y - 6.

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Updated 2026-04-29

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Ch.5 Polynomials and Polynomial Functions - Intermediate Algebra @ OpenStax

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