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. 5 is a ________________________________ m is a _______________________________ 2x² is _________________________________ number variable the product of a number and a variable.

Constant A constant is a number add or subtracted to another term. __________ is the constant in 3x + 4y + 5 __________ is the constant in 2 – 3x 5 2

Coefficient 4 1

Like Term A like term is a term that has the same variable and the same exponents.

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 are ________, they are like terms and can be simplified equal to 9x x

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) 4x 2 y + x 2 y 5x 2 y 4) 3m 2 n + 10mn 2 + 7m 2 n - 4mn 2 10m 2 n + 6mn 2

21a + 6b 6) 4d + 6a 2 - d + 12a 2 18a 2 + 3d 7) y 5) 13a + 8a + 6b

Which of the following is the simplified form of 5x x + 14 ? Answer Now 1.-12x x x x – 18

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

Combine your like terms. 3a 2 + 3ab + 4ab - b 2 + 6b 2 3a 2 + 7ab + 5b 2 Add the following polynomials: (3a 2 + 3ab - b 2 ) + (4ab + 6b 2 )

Subtracting Polynomials Subtracting polynomials is a little different. When subtracting polynomials, change the subtraction sign to _____________ and change all other signs in the _________ polynomials to its ______________. addition SECOND opposite sign

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 Subtract the following polynomials: (9y - 7x + 15a) - (-3y + 8x - 8a)

Rewrite subtraction as adding the opposite. (7a - 10b) + (- 3a - 4b) Group the like terms. 7a - 3a - 10b - 4b 4a - 14b 5. Subtract the following polynomials: (7a - 10b) - (3a + 4b)

Find the sum or difference. (5a – 3b) + (2a + 6b) 1.3a – 9b 2.3a + 3b 3.7a + 3b 4.7a – 3b

Find the sum or difference. (5a – 3b) – (2a + 6b) 1.3a – 9b 2.3a + 3b 3.7a + 3b 4.7a – 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) 5 x x + 35

Distribute 3(m - 4) 3 m m - 12 Distribute -2(y + 3) -2 y + (-2) 3 -2y + (-6) -2y - 6

Distribute 2(x² + 4x²y) + 5(3x² - x²y) 2x² + 8x²y + 15x² - 5x²y 2x² + 15x² + 8x²y – 5x²y 10x² +10x²y

Distribute 4(3y² + 4x²y) + (3y² - xy²) 12y² + 16x²y + 3y² - xy² 12y² + 3y² + 16x²y – xy² 15y² + 16x²y – xy²

Distribute 3(3a² + 12) - 2(a² - 1) 9a² a² + 2 9a² - 2a² a² + 38

Distribute 2(3x² - 6y² + 4x²y) - (3x² + y² - x²y) 6x² - 12y² + 8x²y - 3x² - y² + x²y 6x² - 3x² -12y² - y² + 8x²y + x²y 3x² -13y² + 9x²y