INCHARGE TO EDIT THE MODULE FIRST QUARTERMAAM KATHLEEN ATASAN -including the WHLP, thinking log, answer sheet, answer key, activity sheets SECOND QUARTERMAAM RAINE -including the WHLP, thinking log, answer sheet, answer key, activity sheets THIRD QUARTERMAAM AMPER -including the WHLP, thinking log, answer sheet, answer key, activity sheets FOURTH QUARTERMAAM LAGULAY -including the WHLP, thinking log, answer sheet, answer key, activity sheets INCHARGE FOR THE QUARTER TEST USING GOOGLE FORM FIRST QUARTERMAAM WENDY CAPISIN SECOND QUARTERSIR HALOP THIRD QUARTER- FOURTH QUARTER- The correct answer : 3 3x +13x-16 1. 2. 6x+y+8z Activity 14: Let’s Do Subtraction! Let’s Do It This Way: Subtract honestly the given polynomials below. Subtract horizontally: (7x – 8 ) – (2x + 4) Subtract horizontally: (11a2 – 3a + 4) –(2a2 – a + 1) Subtract vertically:(5y +9) – (8y – 2) Subtract vertically:(5x2 – 8x + 6) - (3x2 – 3x + 2) PALMA Multiplication of Polynomials Let us first review the laws of exponent that can be applied in this lesson. A. Product of Same Bases In multiplying the same base, add the exponents. For example, 1. (x2) (x3) = x2 + 3 2. (23) (24) = 23 + 4 (x2) (x3) = x5 (23) (24) = 27 (23) (24) = 2 x 2 x 2 x 2 x 2 x 2 x 2 (23) (24) = 128 PALMA B. Power to a Power If an exponent is raise by another exponent, multiply the exponents and copy the base. For example, 1. (x2)3 = x2 (3) (x2)3 = x6 2. (23)3 = 23 (3) = 29 =2x2x2x2x2x2x2x2x2 (23)3 = 512 PALMA C. Two bases and an exponent If an exponent is raise to two bases, raise the two bases with the exponent. For example, 1. (ab)2 = (a)2 (b)2 2. (2x)3 = (2)3 (x)3 (ab)2 = a2 b2 = 2 x 2 x 2 (x)3 (2x)3 = 8 x3 PALMA In multiplying polynomials as well, we will also use the distributive property of equality. For example, 1. 2 (a + 1) PALMA Multiply the expression outside the parenthesis to each term of the expression inside the parenthesis and Simplify the equation. 2 (a + 1) = 2 (a) + 2 (1) Therefore, 2 (a + 1) = 2a + 2. Activity 15: Let’s Do This Once Again Let’s Do It This Way: Simplify the given expressions applying laws of exponent and distributive property. A. 1. (s4) (s7) 4. (-3m2)3 2. (23)2 5. (-2ab)2 3. (5n)3 B. 1. 2 (x – 2) 2. b (b + 5) 3. 2c (c – 3) PALMA Multiplying Monomial by a Polynomial 1: Give the product of (2) (b + 3). Using the Distributive Property, this is how you do it. Multiply monomial to the first term of the binomial. (Applying Distributive Property) Multiply monomial to the second term of the binomial. (Using Distributive Property) Therefore, 2 (b + 3) = 2b + 6. (x + 2) (x – 1) = x (x –1)+2 (x–1) (x + 2) (x – 1) = x (x –1)+2 (x–1) Multiplying Polynomial by Polynomial Examples: (x + 2) (x - 1) = ? This example can be presented using the distributive property. This is how to do it. Multiply the first term of the first binomial to the second binomial. Multiply the second term of the first binomial to the second binomial. PALMA (X+2) (x-1)=x(x-1) +2 (x-1) Get the product of PALMA x (x – 1) + 2 (x – 1) x2 -x + = 2x -2 Combine like terms. = x2 – x = x2 + 2x +x –2 –2 Therefore, (x + 2) (x – 1) = x2 + x – 2 Activity 16: Simplify Me Let’s Do It This Way: Find the product of polynomial and polynomial. Show your solution. Number 1 is done for you. 1. (a – 2) (a + 5) Answer:(a – 2)(a + 5) = a (a + 5) + (- 2) (a + 5) = a2 + 5a – 2a – 10 = a2 + 3a – 10 2. (m + 3) (2m – 1) 3. (c – 3) (c2 – 2c + 3) 4. (2x + 1) (x2 – 5x + 2) That PALMA is all about in multiplication of polynomials. subtraction and