Polynomials
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This document discusses algebraic expressions and polynomials. It defines monomials as expressions with one term, binomials as expressions with two terms, and trinomials as expressions with three terms. It provides examples of each. It explains that polynomials with like terms can be simplified by combining them. It also discusses that terms can include numbers, variables, or products of numbers and variables, and that the coefficient is the number multiplied with a variable. It concludes by providing tips and sayings related to learning mathematics.
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1) The binomial theorem states that the terms in the expansion of (a + b)n follow a predictable pattern, with the power of the first term being n and decreasing by 1 for each subsequent term as the power of the second term increases from 0 to n.
2) Pascal's triangle can be used to find the coefficients of the terms in the expansion. For example, the coefficients of the terms in (a + b)3 are the numbers in the 4th row of Pascal's triangle.
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To multiply a binomial and a trinomial:
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- 4. A polynomial that having like terms can be simplified by adding or substracting the like terms. For example : 5a +3b+4c -2a-9c +7b Can be simplified as : (5a-2a) +(3b+ 7b) +(4c-9c) = 3a + 10b +(-5c) =3a +10b -5c The simplest expression
- 6. a. 2s+ 3c+ 4f+ 2s +h +c-s b. n+x+3m +4n-5x+2m grouping the terms : grouping he terms : (3s+2s-s) +(3c+c)+ 4f +h (n +4n)+(x-5x) + The simplest expression : (3m+2m) 4s+4c+4f+h =4(s+c+f) +h = 5n+(-4x)+5m = 5n-4x+5m
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