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P O D. Use mental math to solve:. basic. advanced. 8 × 34. 7 × 231. 8(30) + 8(4). 7(200) + 7(30) + 7(1). 240 + 32. 1400 + 210 + 7. 1617. 272. S i m p l i f y A l g e b r a i c E x p r e s s i o n s.

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  1. POD Use mental math to solve: basic advanced 8 × 34 7 × 231 8(30) + 8(4) 7(200) + 7(30) + 7(1) 240 + 32 1400 + 210 + 7 1617 272

  2. Simplify Algebraic Expressions When addition or subtraction signs separate an algebraic expression into parts, each part is called a term. The numerical factor of a term that contains a variable is called a coefficient of the variable.

  3. Like terms contain the same variables to the same powers. For example 3x and 7x are like terms. So are 8xy2 and 12xy2. A term without a variable is called a constant.

  4. three terms -4x + 12 + x constant like terms

  5. example 6n − 7n − 4 + n Identify the terms: 6n, 7n, 4, n Identify the like terms: 6n, 7n, n Identify the coefficients: 6, 7, 1 Identify the constants: 4

  6. An algebraic expression is in simplest form if it has no like terms and no parenthesis. Use the distributive property to combine like terms. Example: Write 4y + y in simplest form 4y + y = 4y + 1y multiplicative identity property; y=1y (4 + 1)y or 5y distributive property

  7. Example: Write 7x − 2 − 7x + 6 in simplest form 7x − 2 − 7x + 6 = 7x + (-2) + (-7x) + 6 Definition of subtraction = 7x + (-7x) + (-2) + 6 Commutative Property = [(7+ (-7)]x + (-2) + 6 Distributive Property = (0)x + 4 = 0 + 4 = 4 Multiplicative Property of Zero

  8. Whiteboard time Identify the terms, like terms, coefficients, and constants in each expression. 9y − 4 − 11y + 7 terms: 9y, -4, -11y, 7 like terms: 9y and -11y, -4 and 7 coefficients: 9, -11 constants: -4, 7

  9. Whiteboard time Identify the terms, like terms, coefficients, and constants in each expression. 3x + 2 − 10 − 3x terms: 3x, 2, 10, 3x like terms: 3x and 3x, 2 and 10 coefficients: 3, 3 constants: 2, 10

  10. Whiteboard time Write the expression in simplest form 4z − z 4z − 1z (4 − 1)z 3z

  11. Whiteboard time Write the expression in simplest form 6 − 3n + 3n 6 − 0 6

  12. Whiteboard time Write the expression in simplest form 2g − 3 + 11 − 8g 2g + (-3) + 11 + (-8g) 2g + (-8g) + (-3) + 11 (2+ -8)g + 8 -6g + 8

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