Math Tutoring on Multiplying Polynomials
To multiply monomials, we need to multiply the coefficients and then multiply the variables using the product rule for exponents as stated here. Remember, we are allowed to change the order of multiple multiplication due to the commutative property of multiplication. To multiply two polynomials, we multiply each term in one polynomial by each term in the other polynomial and then simplify by combining like terms in right and descending order. To two binomials (a+b) and (c+d) we apply FOIL method, where First terms: ac, Outer terms: ad, Inner terms: bc, Last terms: bd. Another special product is the product of a sum and difference, like (a+b) and (a-b). The product of the sum and difference of the same two terms is the square of the first term minus the square of the second term. (a+b)(a-b) = a² b², this is called a Difference of squares. There are special formulas for the square of binomials: (a+b)² = a² + 2ab + b² and (a-b)² = a² - 2ab + b² .
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1. How do you multiply a monomial by a monomial?
2. How do you multiply a binomial by a binomial?
3. How do you multiply a trinomial by a trinomial?
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