<p> CC Math I Standards: Unit 2 COMBINE LIKE TERMS and DISTRIBUTIVE PROPERTY I. COMBINE LIKE TERMS Step #1: Identify all LIKE TERMS Step #2: COMBINE means ADD or SUBTRACT the COEFFICIENTS Step #3: Answers will keep SAME variables and exponents as originals EXAMPLES: 1) 3 + 4x – 7x2 + 5x 3) 3y + 4 – 2y – 5 + 6y </p><p>2) 8 + 9ab + 3b2 – 2ab + 5a2 + 4 4) 11r – 5 + 3r – 7s + 9 – r </p><p>PRACTICE: 1) 4w4 + w4 + 3w2 – 2w2 3) 5n2 + 11n – 19 + 3n2 – 8 + 7n2</p><p>2) 2x – 7 + 9x + 8x2 – 5x 4) 12z + 5yz - 3z2 + 9z – 7yz – z2 + 6y </p><p>II. DISTRIBUTIVE PROPERTY The distributive property “gets rid of the parentheses” by distributing/ sharing multiplication</p><p>DEFINTION: If a (b + c), then a (b + c) = ab + ac Arrow Method: Box Method: a( b + c) = a (b + c) = </p><p> REMINDER: If no coefficient written, then it’s an invisible 1. HINT: CIRCLE the term being distributed including the positive or negative sign. EXAMPLES : Distributive Property </p><p>1) 6(8 + 3) 4) (-4c + a) (-5) </p><p>2) - 2 (4 + 9z) 5) 3 (5x2 - 7x + 3) </p><p>3) 7(2 - y) 6) (x + 8y – 5) 4</p><p>III. VERBAL EXPRESSIONS WITH THE DISTRIBUTIVE PROPERTY VERBAL ALGEBRAIC EXAMPLE #1: Mr. Smith has three apples and two bananas.</p><p>He wants to double all the fruit that he has.</p><p>That means he must double each kind of fruit he has.</p><p>How much fruit will Mr. Smith have? EXAMPLE #2: A freshman has 1 binder, 2 pencils, and 3 erasers on the first day of school. </p><p>On the next day of school he needs to triple the number of supplies. </p><p>That means the freshman must triple each type of supply.</p><p>How many supplies will freshman have?</p><p>PRACTICE: DISTRIBUTIVE PROPERTY 1) (4y + 5z) 6 2) 5 (2x + 1) 3) –3 ( 7x – 2) 4) –5 (–6 – z) 5) 11 ( a2 + 5ab – 7b2) 6) (5y2 + 3y – 9) (-2) IV. SIMPLIFYING AN EXPRESSION  DISTRIBUTIVE PROPERTY to inside of parentheses only  COMBINE LIKE TERMS EXAMPLES 1) 3 (x + 4) + 2 6) 18 + 7(5x + 2) 7) 11z – 6(2z + 5) </p><p>2) 5(y + 2) – 7y 8) 11a – 3(4a2 – a) – 5a2</p><p>3) 6(3x – 2) – 8 9) 8(5b + 10) – 15b – 35 </p><p>4) - 4 (2x + 9) + 5x 10) – 3 (z + 8y – 5) + 10z – 5y + 9</p><p>5) –9 ( 5r – 3) + 16 11) 4 (7 – 2r – s) + 6rs + 9 + 10s 12) 9xy + 13x – 7(3x – 4xy) CC MATH I Standards: UNIT 2 IN – DEPTH: DISTRIBUTIVE PROPERTY AND COMBINE LIKE TERMS</p><p>I. WARM UP: Simplify each of the following expressions</p><p>1) x + 3 – 5x + 7 + 4y 2) 8(4r + 3) 3) 2z + 7z2 – 9z + 21z3</p><p>4) –3 (5m – 2n + 7) 5) 7 (2r + 6) – 12r 6) –9 (3x – 4) + 7</p><p>II. ADVANCED SIMPLIFYING EXPRESSIONS REMINDER #1: STOP distributing when the parentheses end REMINDER #2: Be careful about the positive or negative sign of multiplications.</p><p>1) 7 – 3(–6 + 3y) + 2y 2) 5(x + 6) + 3(7 + 2x) </p><p>3) 2(5z – 4y) + 7(3 – 2y) 4) x2 + 6(2x + 5) – 7x 5) 3(9r – 2) – 5(3r – 4) 6) 8(2y + 4) – 3(4y + 6)</p><p>7) 2(5a + 3b) – 4(a + 3b) + 8a – 7b 8) 7(3x2 + 8y) – 3(2x – 3x2) – 8x + 4y</p><p>III. DISTRIBUTING VARIABLES Reminder #1: Variables can multiply with other variables = write next to each other  Exp: a  5b  5ab or 3xy  wz  3xywz Reminder #2: Variables times itself = increases the exponent (Exp:  Exp: c  c  c 2 or n  3n3  3n4</p><p>1) d(3b + 5c) 2) – q (– 5 + 11p – 7q2) 3) r(7r + 8) – 6r</p><p>4) t(9s – 4u) + 7ut – 2st 5) x (2y + 7) + y (9 + 5x)</p>