SIMPLIFYING ALGEBRAIC EXPRESSIONS Lesson 21

WARM UP Jack has 3010 songs and 18 videos on his iPod. He downloads 15 new songs and 8 more videos. How many songs and videos does he now have on his iPod? Jack decides to get rid of the songs and videos that he doesn’t like anymore. He deletes 28 songs and 5 videos. How many songs and videos does he have left?

WARM UP- SOLUTIONS Jack has 3010 songs and 18 videos on his iPod. He downloads 15 new songs and 8 more videos. How many songs and videos does he now have on his iPod? = 3025 songs = 26 videos Jack decides to get rid of the songs and videos that he doesn’t like anymore. He deletes 28 songs and 5 videos. How many songs and videos does he have left? 3025 – 28 = 2997 songs 26 – 5 = 21 videos

COMBINING LIKE TERMS When we combine terms we look at the variables (letters) and their exponents. If the variables and exponents are the same then we simply add or subtract the coefficients (numbers in front). 2x + 3y – 5x + 8y 2x – 5x = -3x 3y + 8y = 11y Answer: -3x + 11y

EXAMPLE 1 Which of the following expressions is equivalent to the one shown below? ( b 3 + 5b 2 – 2b) – (b 3 + b – 1) A. 5b 2 – b B. 5b 2 – 3b + 1 C. 4b 2 – b D. 5b 2 – 3b – 1

EXAMPLE 1- SOLUTION Which of the following expressions is equivalent to the one shown below? ( b 3 + 5b 2 – 2b) – (b 3 + b – 1) A. 5b 2 – b B. 5b 2 – 3b + 1 C. 4b 2 – b D. 5b 2 – 3b – 1

EXAMPLE 2 Simplify: 4 y(2x + 8y – 7) A. 8xy + 32y – 28y B. 8xy + 32y 2 – 28y C. 6xy + 32y – 28y D. 6xy + 32y 2 – 28y

EXAMPLE 2- SOLUTION Simplify: 4 y(2x + 8y – 7) A. 8xy + 32y – 28y B. 8xy + 32y 2 – 28y C. 6xy + 32y – 28y D. 6xy + 32y 2 – 28y

EXAMPLE 3 Which is equivalent to (5x 2 – 4x + 1) + (-7x + 2)? A. -2x 2 + 6x + 1 B. 5x 2 – 3x – 1 C. 5x 2 – 3x + 3 D. 5x x + 3

EXAMPLE 3- SOLUTION Which is equivalent to (5x 2 – 4x + 1) + (-7x + 2)? A. -2x 2 + 6x + 1 B. 5x 2 – 3x – 1 C. 5x 2 – 3x + 3 D. 5x x + 3

EXAMPLE 4 If 2 a 2 – 6a + 5 is subtracted from 3a 2 – 2a + 3, the result is A. 5a 2 – 8a + 8. B. a 2 + 4a – 2. C. -a 2 – 4a + 2. D. a 2 – 8a + 8.

EXAMPLE 4- SOLUTION If 2 a 2 – 6a + 5 is subtracted from 3a 2 – 2a + 3, the result is A. 5a 2 – 8a + 8. B. a 2 + 4a – 2. C. -a 2 – 4a + 2. D. a 2 – 8a a 2 – 2a + 3 – (2a 2 – 6a + 5) = 3a 2 – 2a + 3 – 2a 2 + 6a – 5 = a 2 + 4a – 2

EXAMPLE 5 Simplify: -4b(-3a + 2b + 6c) A. 12ab + 8b bc B. 12ab – 8b 2 – 24bc C. -12ab + 8b bc D. 12ab – 8b 2 – 24bc

EXAMPLE 5- SOLUTION Simplify: -4b(-3a + 2b + 6c) A. 12ab + 8b bc B. 12ab – 8b 2 – 24bc C. -12ab + 8b bc D. 12ab – 8b 2 – 24bc

EXAMPLE 6 Which of the following is equivalent to the expression below? ( x + 5)(2x – 3) A. 2x 2 + 7x – 15 B. 2x 2 – 7x – 15 C. 3x 2 + 7x – 15 D. 3x 2 – 7x – 15

EXAMPLE 6 Which of the following is equivalent to the expression below? ( x + 5)(2x – 3) A. 2x 2 + 7x – 15 B. 2x 2 – 7x – 15 C. 3x 2 + 7x – 15 D. 3x 2 – 7x – 15

EXAMPLE 7 Which of the following is equivalent to the expression below? (3x + 6y) + (2x – y) A. 5x – y B. 5x + 7y C. 6x – 6y D. 5x + 5y

EXAMPLE 7- SOLUTION Which of the following is equivalent to the expression below? (3x + 6y) + (2x – y) A. 5x – y B. 5x + 7y C. 6x – 6y D. 5x + 5y 3x + 2x + 6y – y = 5x + 5y

EXAMPLE 8 Which is equivalent to (2a + 3b – 2c) + (3a – 4b – c) + (a – 5b + 4c)? A. 5a – 6b + c B. 6a – 6b – c C. 6a – 6b + c D. 6a 2 – 6b 2 + c 2

EXAMPLE 8- SOLUTION Which is equivalent to (2a + 3b – 2c) + (3a – 4b – c) + (a – 5b + 4c)? A. 5a – 6b + c B. 6a – 6b – c C. 6a – 6b + c D. 6a 2 – 6b 2 + c 2

EXAMPLE 9 Simplify the expression below. -2a(-3a + 4b – 5) A. -5a 2 + 8ab + 10a B. -6a 2 – 8ab – 10a C. 6a 2 – 8ab + 10a D. 5a 2 + 8ab – 10a

EXAMPLE 9- SOLUTION Simplify the expression below. -2a(-3a + 4b – 5) A. -5a 2 + 8ab + 10a B. -6a 2 – 8ab – 10a C. 6a 2 – 8ab + 10a D. 5a 2 + 8ab – 10a

EXAMPLE 10 Which of the following is equivalent to the expression below? (x – 2)(2x 2 + 3) + x 3 – 2x A. 3x 3 – 2x – 6 B. 3x 3 + x – 6 C. 3x 3 – x 2 – 2x – 6 D. 3x 3 – 4x 2 + x – 6

EXAMPLE 10- SOLUTION Which of the following is equivalent to the expression below? (x – 2)(2x 2 + 3) + x 3 – 2x A. 3x 3 – 2x – 6 B. 3x 3 + x – 6 C. 3x 3 – x 2 – 2x – 6 D. 3x 3 – 4x 2 + x – 6

EXAMPLE 11 Which of the following expressions is equivalent to the one shown below? ( x – 3) (2x + 5) A. 2x 2 – x – 15 B. 2x 2 – 15 C. 2x x – 15 D. 2x 2 + 2

EXAMPLE 11- SOLUTION Which of the following expressions is equivalent to the one shown below? ( x – 3) (2x + 5) A. 2x 2 – x – 15 B. 2x 2 – 15 C. 2x x – 15 D. 2x 2 + 2

EXAMPLE 12 Which of the following is equivalent to the expression below? (3x – 2)(2x + 3) A. 5x 2 + 5x + 1 B. 5x x + 1 C. 6x x – 6 D. 6x 2 + 5x – 6

EXAMPLE 12- SOLUTION Which of the following is equivalent to the expression below? (3x – 2)(2x + 3) A. 5x 2 + 5x + 1 B. 5x x + 1 C. 6x x – 6 D. 6x 2 + 5x – 6

EXAMPLE 13 Which is equivalent to p 6 p 2 ? A. p 8 B. 2p 8 C. p 10 D. p 12

EXAMPLE 13- SOLUTION Which is equivalent to p 6 p 2 ? A. p 8 B. 2p 8 C. p 10 D. p 12

EXAMPLE 14 Which of the following is equivalent to the expression below? (5x + 6y – 3z) + (3x – 8y + z) A. 8x – 14y – 4z B. 8x – 2y – 2z C. 8x – 14y – 2z D. 8x – 2y – 3z

EXAMPLE 14- SOLUTION Which of the following is equivalent to the expression below? (5x + 6y – 3z) + (3x – 8y + z) A. 8x – 14y – 4z B. 8x – 2y – 2z C. 8x – 14y – 2z D. 8x – 2y – 3z

EXAMPLE 15 Which of the following is equivalent to the expression below? (7 a 2 + 5a + 3) + (–3a 2 + 2a – 4) A. 4a 2 + 7a – 1 B. 4a 2 + 7a + 1 C. –4a 2 + 7a – 1 D. –4a 2 + 7a + 1

EXAMPLE 15- SOLUTION Which of the following is equivalent to the expression below? (7 a 2 + 5a + 3) + (–3a 2 + 2a – 4) A. 4a 2 + 7a – 1 B. 4a 2 + 7a + 1 C. –4a 2 + 7a – 1 D. –4a 2 + 7a + 1

EXAMPLE 16 Ben's Bakery charges a fee of 2d + 25 to deliver d boxes of baked goods while Dan's Bakery charges 3d Which expression describes how much more Dan's Bakery charges than Ben's Bakery? A. 5d + 45 B. d – 5 C. d + 5 D. -d + 5

EXAMPLE 16- SOLUTION Ben's Bakery charges a fee of 2d + 25 to deliver d boxes of baked goods while Dan's Bakery charges 3d Which expression describes how much more Dan's Bakery charges than Ben's Bakery? A. 5d + 45 B. d – 5 C. d + 5 D. -d + 5