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How to Multiply Trinomials by Trinomials?

TopWe know that Polynomials are algebraic expressions with varying number of terms. If the number of terms is only one, we call it a monomial, with two terms an algebraic expression is called a binomial, those with three terms are called trinomials & if the number of terms exceed three, it is called a polynomial.
Like Numbers we can do mathematical operations on polynomials as well. Just like we can add, subtract, multiply or divide numbers with different number of digits; we can do all mathematical operations with different Types of Polynomials. Let us learn how to multiply trinomials by trinomials.
A trinomial as already mentioned is an algebraic expression with 3 terms. So, to multiply two trinomials we take the first term of the first trinomial & multiply it by the other trinomial using distributive property. Then we take the second term of the first trinomial again & multiply it also with the second trinomial using distributive property and the same steps we follow with the third term of the first trinomial. Thus, we get three Sets of distributive property. After carrying the three distributive sets, we collect the like terms together & add or subtract them according to the signs that precede each of the terms. Thus, finally we get a polynomial with all the like terms combined together. This polynomial is the product of the initial two trinomials.
Example: (2x + 3y - 4xy) * (3x + 5y + 2xy),
= 2x * (3x + 5y + 2xy) + 3y * (3x + 5y + 2xy) – 4xy * (3x + 5y + 2xy),
= 6x2 + 10xy + 4x2y + 9xy + 15y2 + 6xy2 - 12x2y - 20xy2 - 8x2y2,
= 6x2 + 19xy -8x2y +15y2 -14xy2 - 8x2y2.