Adding & Subtracting Polynomial Expressions
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1 Adding & Subtracting Polynomial Expressions A polynomial is a single term or the sum of two or more terms containing variables with exponents that are positive integers. Polynomials are ADDED or SUBTRACTED by combining like terms. Like terms are variable or the same group of variables raised to the same exponent. Aug PM 1
2 Below are examples of terms that are like terms the terms in each group have the same variable or variable group and exponent. Jul PM 2
3 Example 1 Given the expressions below state the reason why the terms in each group are NOT like terms. Jul PM 3
4 First term has an x variable and the second term does not. Both terms have an x variable, but the x variable does not have the same exponent for both terms. Both terms are have the same exponent, but have different variables. Both terms have the same variable group xy, but the x variable & y variable are being raised to different exponents in each term. Jul PM 4
5 When combining like terms just ADD the coefficient(the number in front of the variable or variable group) of each like term but keep the variable and exponent the SAME. Add the coefficients Keep the variable and exponent the same. Write a 1 if for any variable where you do not see a coefficient. Add the coefficients Keep the variable and exponent the same. Jul PM 5
6 Example 2 Simplify Any term where you do not see a coefficient place a 1 in front of the variable. Add the coefficients of the like terms. Rewrite the expression in standard form of a polynomial expression. (Terms are ordered from the highest to lowest exponent.) Jul PM 6
7 Example 3 Simplify Any term where you do not see a coefficient place a 1 in front of the variable. Group the like terms together. Add the coefficients of the like terms. Rewrite the expression in standard form of a polynomial expression. (Terms are ordered from the highest to lowest exponent.) Jul PM 7
8 Example 4 Simplify Any term where you do not see a coefficient place a 1 in front of the variable. Add the coefficients of the like terms. Rewrite the expression in standard form of a polynomial expression. (Terms are ordered from the highest to lowest exponent.) Jul PM 8
9 Example 5 Simplify Any term where you do not see a coefficient place a 1 in front of the variable. Place a 1 in front of the parentheses of the second expression. Drop the parentheses on the first expression, and mutliply each term in the second expression by 1. Whenever any expression is multiplied by positive 1 the expression will remain the same. Jul AM 9
10 Group the like terms together. Add the coefficients of the like terms. Rewrite the expression in standard form of a polynomial expression. (Terms are ordered from the highest to lowest exponent.) Jul AM 10
11 Example 6 Simplify Any term where you do not see a coefficient place a 1 in front of the variable. Place a 1 in front of the parentheses of the second expression. Drop the parentheses on the first expression, and mutliply each term in the second expression by 1. Whenever any expression is multiplied by 1 the expression will remain the same. The only thing that will change is the sign of the expression will now be the opposite. Jul AM 11
12 Group the like terms together. Add the coefficients of the like terms. Rewrite the expression in standard form of a polynomial expression. (Terms are ordered from the highest to lowest exponent.) Jul AM 12
13 Example 7 Use the formula P = 2l + 2w to write a polynomial expression to represent the perimeter of a rectangle with a length of 4x 7 and a width of 3x + 5. P = 2l + 2w Substitute the expression for the length(l) and width(w) into the variables l & w. P = 2(4x 7)+ 2(3x + 5) Mutliply each term in the first parentheses by 2, then multiply each term in second parentheses by 2. P = 2(4x 7) + 2(3x + 5) P = 8x x + 10 Group the like terms together. P = (8 + 6)x ( ) Add the coefficients of the like terms. P = 14x 4 Jul PM 13
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