COMBINE LIKE TERMS and DISTRIBUTIVE PROPERTY

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

2) 8 + 9ab + 3b2 – 2ab + 5a2 + 4 4) 11r – 5 + 3r – 7s + 9 – r

PRACTICE: 1) 4w4 + w4 + 3w2 – 2w2 3) 5n2 + 11n – 19 + 3n2 – 8 + 7n2

2) 2x – 7 + 9x + 8x2 – 5x 4) 12z + 5yz - 3z2 + 9z – 7yz – z2 + 6y

II. DISTRIBUTIVE PROPERTY The distributive property “gets rid of the parentheses” by distributing/ sharing multiplication

DEFINTION: If a (b + c), then a (b + c) = ab + ac Arrow Method: Box Method: a( b + c) = a (b + c) =

 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

1) 6(8 + 3) 4) (-4c + a) (-5)

2) - 2 (4 + 9z) 5) 3 (5x2 - 7x + 3)

3) 7(2 - y) 6) (x + 8y – 5) 4

III. VERBAL EXPRESSIONS WITH THE DISTRIBUTIVE PROPERTY VERBAL ALGEBRAIC EXAMPLE #1: Mr. Smith has three apples and two bananas.

He wants to double all the fruit that he has.

That means he must double each kind of fruit he has.

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.

On the next day of school he needs to triple the number of supplies.

That means the freshman must triple each type of supply.

How many supplies will freshman have?

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)

2) 5(y + 2) – 7y 8) 11a – 3(4a2 – a) – 5a2

3) 6(3x – 2) – 8 9) 8(5b + 10) – 15b – 35

4) - 4 (2x + 9) + 5x 10) – 3 (z + 8y – 5) + 10z – 5y + 9

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

I. WARM UP: Simplify each of the following expressions

1) x + 3 – 5x + 7 + 4y 2) 8(4r + 3) 3) 2z + 7z2 – 9z + 21z3

4) –3 (5m – 2n + 7) 5) 7 (2r + 6) – 12r 6) –9 (3x – 4) + 7

II. ADVANCED SIMPLIFYING EXPRESSIONS REMINDER #1: STOP distributing when the parentheses end REMINDER #2: Be careful about the positive or negative sign of multiplications.

1) 7 – 3(–6 + 3y) + 2y 2) 5(x + 6) + 3(7 + 2x)

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)

7) 2(5a + 3b) – 4(a + 3b) + 8a – 7b 8) 7(3x2 + 8y) – 3(2x – 3x2) – 8x + 4y

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

1) d(3b + 5c) 2) – q (– 5 + 11p – 7q2) 3) r(7r + 8) – 6r

4) t(9s – 4u) + 7ut – 2st 5) x (2y + 7) + y (9 + 5x)