Multiplying A Binomial And A Trinomial
Multiply a binomial by a trinomial in Grade 9 Algebra using the distributive property. Distribute each term of the binomial across all three trinomial terms, then combine like terms.
Key Concepts
Property To multiply a binomial and a trinomial, use the distributive property. Multiply each term in the binomial by the entire trinomial, then combine the resulting products. $$(a+b)(c+d+e) = a(c+d+e) + b(c+d+e)$$.
Explanation This is just a bigger distribution party! Take the first term from the binomial and 'share' it with all three terms in the trinomial. Then, do the exact same thing with the second term from the binomial. Finally, add all the products together and simplify for your final answer.
Examples $(2x+3)(x^2 5x 2) = 2x(x^2 5x 2) + 3(x^2 5x 2) = 2x^3 10x^2 4x + 3x^2 15x 6 = 2x^3 7x^2 19x 6$ $(x 5)(3x^2+2x 4) = x(3x^2+2x 4) 5(3x^2+2x 4) = 3x^3+2x^2 4x 15x^2 10x+20 = 3x^3 13x^2 14x+20$.
Common Questions
What is Multiplying A Binomial And A Trinomial in Grade 9 Algebra?
Property To multiply a binomial and a trinomial, use the distributive property Mastering this concept builds a foundation for advanced algebra topics.
How do you approach Multiplying A Binomial And A Trinomial problems step by step?
Multiply each term in the binomial by the entire trinomial, then combine the resulting products Use this method consistently to avoid common errors.
What is a common mistake when studying Multiplying A Binomial And A Trinomial?
Explanation This is just a bigger distribution party Always check your work by substituting back into the original problem.