Page 681 #25-29 Pre-Algebra HOMEWORK Subtracting Polynomials 13-4

Pre-Algebra 13-1 Polynomials Our Learning Goal Students will be able to classify, simplify, add and subtract polynomials.

Pre-Algebra 13-1 Polynomials Students will be able to classify, simplify, add and subtract polynomials by completing the following assignments. Learn to classify polynomials by degree and by the number of terms. Learn to simplify polynomials. Learn to add polynomials. Learn to subtract polynomials. …..and that’s all folks!

Today’s Learning Goal Assignment 13-4 Subtracting Polynomials Today’s Learning Goal Assignment Learn to subtract polynomials. Pre-Algebra

Subtracting Polynomials 13-4 Subtracting Polynomials Warm Up Problem of the Day Lesson Presentation Pre-Algebra

Subtracting Polynomials 13-4 Subtracting Polynomials Warm Up Write the opposite of each integer. 1. 10 Subtract. 3. 19 – (–12) Add. 5. (3x2 + 7) + (x2 – 3x) 6. (2m2 – 3m) + (–5m2 + 2) –10 2. –7 7 31 4. –16 – 21 –37 4x2 – 3x + 7 –3m2 – 3m + 2 Pre-Algebra

Subtracting Polynomials 13-4 Subtracting Polynomials Problem of the Day Tara has 4 pairs of shorts, 3 tops, and 2 pairs of sandals. If she wants to wear a completely different outfit than she wore yesterday, how many combinations does she have to choose from? 6 Pre-Algebra

Subtracting Polynomials 13-4 Subtracting Polynomials Learn to subtract polynomials. Pre-Algebra

Subtracting Polynomials 13-4 Subtracting Polynomials Subtraction is the opposite of addition. To subtract a polynomial, you need to find its opposite. Pre-Algebra

Additional Example 1A & 1B: Finding the Opposite of a Polynomial 13-4 Subtracting Polynomials Additional Example 1A & 1B: Finding the Opposite of a Polynomial Find the opposite of each polynomial. A. 8x3y4z2 –(8x3y4z2) –8x3y4z2 The opposite of a is –a. B. –3x4 + 8x2 –(–3x4 + 8x2) 3x4 – 8x2 Distribute the sign. Pre-Algebra

Insert Lesson Title Here 13-4 Subtracting Polynomials Insert Lesson Title Here Try This: Example 1A & 1B Find the opposite of each polynomial. A. 4d2e3f3 –(4d2e3f3) –4d2e3f3 The opposite of a is –a. B. –4a2 + 4a4 –(–4a2 + 4a4) 4a2 – 4a4 Distribute the sign. Pre-Algebra

Additional Example 1C: Finding the Opposite of a Polynomial 13-4 Subtracting Polynomials Additional Example 1C: Finding the Opposite of a Polynomial Find the opposite of the polynomial. A. 9a6b4 + a4b2 – 1 –(9a6b4 + a4b2 – 1) –9a6b4 – a4b2 + 1 Distribute the sign. Pre-Algebra

Insert Lesson Title Here 13-4 Subtracting Polynomials Insert Lesson Title Here Try This: Example 1C Find the opposite of the polynomial. A. 9a6b4 + a4b2 – 1 –(9a6b4 + a4b2 – 1) –9a6b4 – a4b2 + 1 Distribute the sign. Pre-Algebra

Subtracting Polynomials 13-4 Subtracting Polynomials To subtract a polynomial, add its opposite. Pre-Algebra

Additional Example 2A: Subtracting Polynomials Horizontally 13-4 Subtracting Polynomials Additional Example 2A: Subtracting Polynomials Horizontally Subtract. A. (5x2 + 2x – 3) – (3x2 + 8x – 4) Add the opposite. = (5x2 + 2x – 3) + (–3x2 – 8x + 4) Associative property. = 5x2 + 2x – 3 – 3x2 – 8x + 4 = 2x2 – 6x + 1 Combine like terms. Pre-Algebra

Insert Lesson Title Here 13-4 Subtracting Polynomials Insert Lesson Title Here Try This: Example 2A Subtract. A. (2y3 + 3y + 5) – (4y3 + 3y + 5) Add the opposite. = (2y3 + 3y + 5) + (–4y3 – 3y – 5) Associative property. = 2y3 + 3y + 5 – 4y3 – 3y – 5 = –2y3 Combine like terms. Pre-Algebra

Additional Example 2B: Subtracting Polynomials Horizontally 13-4 Subtracting Polynomials Additional Example 2B: Subtracting Polynomials Horizontally Subtract. B. (b2 + 4b – 1) – (7b2 – b – 1) = (b2 + 4b – 1) + (–7b2 + b + 1) Add the opposite. Associative property. = b2 + 4b – 1 –7b2 + b + 1 = –6b2 + 5b Combine like terms. Pre-Algebra

Insert Lesson Title Here 13-4 Subtracting Polynomials Insert Lesson Title Here Try This: Example 2B Subtract. B. (c3 + 2c2 + 3) – (4c3 – c2 – 1) = (c3 + 2c2 + 3) + (–4c3 + c2 + 1) Add the opposite. = c3 + 2c2 + 3 – 4c3 + c2 + 1 Associative property. = –3c3 + 3c2 + 4 Combine like terms. Pre-Algebra

Subtracting Polynomials 13-4 Subtracting Polynomials You can also subtract polynomials in a vertical format. Write the second polynomial below the first one, lining up the decimal points. Pre-Algebra

Additional Example 3A: Subtracting Polynomials Vertically 13-4 Subtracting Polynomials Additional Example 3A: Subtracting Polynomials Vertically Subtract. A. (2n2 – 4n + 9) – (6n2 – 7n + 5) (2n2 – 4n + 9) 2n2 – 4n + 9 – (6n2 – 7n + 5) + –6n2 + 7n – 5 Add the opposite. –4n2 + 3n + 4 Pre-Algebra

Insert Lesson Title Here 13-4 Subtracting Polynomials Insert Lesson Title Here Try This: Example 3A Subtract. A. (4r3 + 4r + 6) – (6r3 + 3r + 3) (4r3 + 4r + 6) 4r3 + 4r + 6 – (6r3 + 3r + 3) + –6r3 – 3r – 3 Add the opposite. –2r3 + r + 3 Pre-Algebra

Additional Example 3B: Subtracting Polynomials Vertically 13-4 Subtracting Polynomials Additional Example 3B: Subtracting Polynomials Vertically Subtract. B. (10x2 + 2x – 7) – (x2 + 5x + 1) (10x2 + 2x – 7) 10x2 + 2x – 7 – (x2 + 5x + 1) + –x2 – 5x – 1 Add the opposite. 9x2 – 3x – 8 Pre-Algebra

Insert Lesson Title Here 13-4 Subtracting Polynomials Insert Lesson Title Here Try This: Example 3B Subtract. B. (13y2 – 2x + 5) – (y2 + 5x – 9) (13y2 – 2x + 5) 13y2 – 2x + 5 – (y2 + 5x – 9) + –y2 – 5x + 9 Add the opposite. 12x2 – 7x + 14 Pre-Algebra

Additional Example 3C: Subtracting Polynomials Vertically 13-4 Subtracting Polynomials Additional Example 3C: Subtracting Polynomials Vertically Subtract. C. (6a4 – 3a2 – 8) – (–2a4 + 7) (6a4 – 3a2 – 8) 6a4 – 3a2 – 8 – (–2a4 + 7) + 2a4 – 7 Add the opposite. 8a4 – 3a2 – 15 Pre-Algebra

Insert Lesson Title Here 13-4 Subtracting Polynomials Insert Lesson Title Here Try This: Example 3C Subtract. C. (5x2 + 2x + 5) – (–3x2 – 7x) (5x2 + 2x + 5) 5x2 + 2x + 5 – (–3x2 – 7x) +3x2 + 7x Add the opposite. 8x2 + 9x + 5 Pre-Algebra

Additional Example 4: Business Application 13-4 Subtracting Polynomials Additional Example 4: Business Application Suppose the cost in dollars of producing x bookcases is given by the polynomial 250 + 128x, and the revenue generated from sales is given by the polynomial 216x – 75. Find a polynomial expression for the profit from producing and selling x bookcases, and evaluate the expression for x = 95. 216x – 75 – (250 + 128x) revenue – cost 216x – 75 + (–250 – 128x) Add the opposite. 216x – 75 – 250 – 128x Associative Property Combine like terms. 88x – 325 Pre-Algebra

Additional Example 4 Continued 13-4 Subtracting Polynomials Additional Example 4 Continued The profit is given by the polynomial 88x – 325. For x = 95, 88(95) – 325 = 8360 – 325 = 8035 The profit is $8035. Pre-Algebra

Insert Lesson Title Here 13-4 Subtracting Polynomials Insert Lesson Title Here Try This: Example 4 Suppose the cost in dollars of producing x baseball bats is given by the polynomial 6 + 12x, and the revenue generated from sales is given by the polynomial 35x – 5. Find a polynomial expression for the profit from producing and selling x baseball bats, and evaluate the expression for x = 50. 35x – 5 – (6 + 12x) revenue – cost 35x – 5 + (–6 – 12x) Add the opposite. 35x – 5 – 6 – 12x Associative Property 23x – 11 Combine like terms. Pre-Algebra

Subtracting Polynomials Insert Lesson Title Here 13-4 Subtracting Polynomials Insert Lesson Title Here Try This: Example 4 Continued The profit is given by the polynomial 23x – 11. For x = 50, 23(50) – 11 = 1150 – 11 = 1139 The profit is $1139. Pre-Algebra

Subtracting Polynomials Insert Lesson Title Here 13-4 Subtracting Polynomials Insert Lesson Title Here Lesson Quiz Find the opposite of each polynomial. Subtract. 3. (3z2 – 7z + 6) – (2z2 + z – 12) 1. 3a2b2c3 –3a2b2c3 2. –3m3 + 2m2n 3m3 – 2m2n z2 – 8z + 18 4. –18h3 – (4h3 + h2 – 12h + 2) 5. (3b2c + 5bc2 – 8b2) – (4b2c + 2bc2 – c2) – 22h3 – h2 + 12h – 2 – b2c + 3bc2 – 8b2 + c2 Pre-Algebra