SWBAT… use the distributive property to simplify expressions Tues, 8/28 Agenda Warm-up (10 min) CLT and Distributive property (30 min) OYO (On Your Own) practice problems (10 min) Warm-Up: Evaluate the expressions when x = -3 and y = -5 1.) 2x2 – y + x 2.) x3 + y2 3.) HW#2: Simplifying Algebraic Expressions 1.) 2x2 – y + x 2(-3)2 – (-5) + (-3) 2(9) + 5 + (-3) 18 + 5 + (-3) 20 2.) x3 + y2 (-3)3 + (-5)2 -27 + 25 -2 3.) 4/5x – 2 2/5 4/5(-3) – 12/5 -12/5 – 12/5 -24/5 -4 4/5
Simplifying Algebraic Expressions by Combining Like Terms Infinity HS Ms. Sophia Papaefthimiou
Like Terms are terms with the same variable AND the same exponent.
Are these like terms? 1) 13x, 22x 2) 5ab, 4ba 3) 5x, 25 Yes, the variables and exponents are the same. 2) 5ab, 4ba Yes, the order of the variables doesn’t matter. (ab = ba. Commandment #9) 3) 5x, 25 No, the 25 does not have a variable x
1.) Which of the following is the simplified form of -4x + 7x ? Don’t forget the negative!
2.) Which of the following is the simplified form of 5x – 4 – 7x + 14 ?
3.) Which of the following is the simplified form of 5x – 4x2 – 7x + 14x2 ?
3.) -4d – 6a2 +2d – 12a2 -18a2 – 2d 4.) 5.) y
Simplifying Algebraic Expressions using the Distributive Property Infinity HS Ms. Sophia Papaefthimiou
The Distributive Property The process of distributing by multiplying the number and/or variable on the outside of the parentheses to each term on the inside. a(b + c) a(b + c) = ab + ac a(b – c) a(b – c) = ab – ac Example #1 5(x + 7) (5)(x) + (5)(7) 5x + 35
3(m – 4) (3)(m) – (3)(4) 3m – 12 -2(y + 3) (-2)(y) + (-2)(3) Example #2 3(m – 4) (3)(m) – (3)(4) 3m – 12 Example #3 -2(y + 3) (-2)(y) + (-2)(3) -2y + (-6) -2y – 6
-5(z – 9) (-5)(z) – (-5)(9) -5z + 45 -(n2 + n – 25) Example #4 -5(z – 9) (-5)(z) – (-5)(9) -5z + 45 Example #5 -(n2 + n – 25) (-1)(n2) + (-1)(n) – (-1)(25) -n2 – n + 25
Which statement demonstrates the distributive property incorrectly? 3(x + y + z) = 3x + 3y + 3z (a + b)c = ac + bc 5(2 + 3x) = 10 + 3x 6(3k – 4) = 18k – 24 Answer Now
p = 10t – 100 p = -10t p = 7t – 15 p = 10t – 20 Answer Now The algebraic rule p = 5(2t – 20) expresses the profit, p, for a school dance in terms of the number tickets sold, t. Which is an equivalent form of this rule? p = 10t – 100 p = -10t p = 7t – 15 p = 10t – 20 Answer Now
Let’s put distributive property and CLT together! 5(z – 3) + 4z (HW#2, Prob #9) 5z – 15 + 4z 9z – 15 4(y2 + 8y – 2) – y2 + y 4y2 + 32y – 8 – y2 + y 3y2 + 33y – 8 5(3x – 7) – 6x (HW#2, Prob #12) 15x – 35 – 6x 9x – 35
Simplify each expression 1) 5a2 + 7a Simplified 2) -4x2y + x2y – x2y + x2 -4x2y + x2 3) a + 3a – 4(9 – a) 8a – 36 4) If a triangle has sides 3x – 2, 5 – x and 2x – 5, what is the perimeter of the triangle? 4x – 2
SWBAT… simplify algebraic expressions Wed, 8/29 Agenda Warm-up (15 min) Review HW#1 & 2 (35 min) Warm-Up: Simplify: -3x(x3 – 2x2) 7(4x2 + 3x) – 2(5x2 + x) 6x + 4[7 – (x – 2)] (First distribute -1) Back of agenda problems: Quiz tomorrow 1. 3x4 + 6x3 28x2 + 21x – 10x2 – 2x (now CLT) 18x2 + 19x (HW#2, Problem #15) 17
Simplify -x2 – 3xy + 4y3 for x = -3 and y = -1 Practice Problems: Simplify for x = -2 and y = 4 Simplify -x2 – 3xy + 4y3 for x = -3 and y = -1 Simplify 10y2 – 1 for y = √8 (square root of 8) -22 79 18
SWBAT… simplify algebraic expressions Fri, 8/31 Agenda WU (5 min) Quiz (30 min) Two-step equations Warm-Up: Simplify: Evaluate -x2 – 3xy + 4y2 for x = -3, y = -1 Simplify -x2 – 3x + 4x2 – x2 + 10x -14 2x2 + 7x 19