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Combining Like Terms, Add/Sub Polynomials and Distributing Tammy Wallace Varina High Term A term is a number, variable, or the product of numbers and variables. number 5 is a ________________________________ variable m is a _______________________________ the product of a number and a variable. 2x² is _________________________________ Constant A constant is a number add or subtracted to another term. 5 __________ is the constant in 3x + 4y + 5 2 __________ is the constant in 2 â 3x Coefficient A coefficient is the numerical part multiplied in front of a variable. 4 is the coefficient in front of 4a ______ 1 is the coefficient in front of y² ______ ð ð ______ is the coefficient in front of 5ðĶ 2 7 Like Term A like term is a term that has the same variable and the same exponents. 13k and 22k 5ab and 4ba 3ðĨðĶ 2 and ðĨðĶ 2 Simplifying Expressions To simplify an expression means to add or subtract the coefficients of all like terms based on the operation in front of each term. Simplify 3x + 6x Because both terms have the same variables which x are ________, they are like terms and can be simplified equal to 9x Simplify 8x² + 2x² + 5y + y Are there any like terms? Yes Which ones? 8x² is a like term with 2x² and 5y is a like term with y Therefore, once combined, the expression is simplified to 10x² + 6y Simplify 1) 5a + 7a 12a 2) 6.1y - 3.2y 2.9y 3) 4x2y + x2y 5x2y 4) 3m2n + 10mn2 + 7m2n - 4mn2 10m2n + 6mn2 5) 13a + 8a + 6b 21a + 6b 6) 4d + 6a2 - d + 12a2 18a2 + 3d 3y y 7) ïŦ 4 4 y Which of the following is the simplified form of 5x - 4 - 7x + 14 ? 1. 2. 3. 4. -12x + 10 -2x + 10 2x - 18 12x â 18 Answer Now Polynomial A polynomial is a group of two or more terms. Add the following polynomials: (9y - 7x + 15a) + (-3y + 8x - 8a) Group your like terms and simplify 9y - 3y - 7x + 8x + 15a - 8a 6y + x + 7a Add the following polynomials: (3a2 + 3ab - b2) + (4ab + 6b2) Combine your like terms. 3a2 + 3ab + 4ab - b2 + 6b2 2 2 3a + 7ab + 5b Subtracting Polynomials Subtracting polynomials is a little different. When subtracting polynomials, change the addition and change all other subtraction sign to _____________ SECOND polynomials to its ______________. opposite sign signs in the _________ Subtract the following polynomials: (9y - 7x + 15a) - (-3y + 8x - 8a) Rewrite subtraction as adding the opposite. (9y - 7x + 15a) + (+ 3y - 8x + 8a) Group the like terms. 9y + 3y - 7x - 8x + 15a + 8a 12y - 15x + 23a 5. Subtract the following polynomials: (7a - 10b) - (3a + 4b) Rewrite subtraction as adding the opposite. (7a - 10b) + (- 3a - 4b) Group the like terms. 7a - 3a - 10b - 4b 4a - 14b Find the sum or difference. (5a â 3b) + (2a + 6b) 1. 2. 3. 4. 3a â 9b 3a + 3b 7a + 3b 7a â 3b Find the sum or difference. (5a â 3b) â (2a + 6b) 1. 2. 3. 4. 3a â 9b 3a + 3b 7a + 3b 7a â 9b Distributive Property The Distributive Property is the process of multiplying a number directly outsides of the parenthesis by everything inside the parenthesis. Example 5(x + 7) 5âĒx+5âĒ7 5x + 35 Distribute 3(m - 4) 3âĒm-3âĒ4 3m - 12 Distribute -2(y + 3) -2 âĒ y + (-2) âĒ 3 -2y + (-6) -2y - 6 Distribute 2(x² + 4x²y) + 5(3x² - x²y) 2x² + 8x²y + 15x² - 5x²y 2x² + 15x² + 8x²y â 5x²y 10x² +10x²y Distribute 4(3y² + 4x²y) + (3y² - xy²) 12y² + 16x²y + 3y² - xy² 12y² + 3y² + 16x²y â xy² 15y² + 16x²y â xy² Distribute 3(3a² + 12) - 2(a² - 1) 9a² + 36 - 2a² + 2 9a² - 2a² + 36 + 2 7a² + 38 Distribute 2(3x² - 6y² + 4x²y) - (3x² + y² - x²y) 6x² - 12y² + 8x²y - 3x² - y² + x²y 6x² - 3x² -12y² - y² + 8x²y + x²y 3x² -13y² + 9x²y