This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions for questions 1 and 2. 1. Simplify the following expressions: 1.1 5a + 4c - 3a + c + 2 - 4c + 4 Step 1: Group like terms. (5a - 3a) + (4c + c - 4c) + (2 + 4) Step 2: Combine like terms. 2a + c + 6 The simplified expression is 2a + c + 6. 1.2 -3xy + x + 2y + 4xy + 3x - 2xy + y Step 1: Group like terms. (-3xy + 4xy - 2xy) + (x + 3x) + (2y + y) Step 2: Combine like terms. (-3+4-2)xy + (1+3)x + (2+1)y -xy + 4x + 3y The simplified expression is -xy + 4x + 3y. 1.3 2a^2 + 4a + 7 - 3a^2 - 2a + 7 Step 1: Group like terms. (2a^2 - 3a^2) + (4a - 2a) + (7 + 7) Step 2: Combine like terms. -a^2 + 2a + 14 The simplified expression is -a^2 + 2a + 14. 1.4 3ab + a - 6ab + 6a + b - 4a - 2b Step 1: Group like terms. (3ab - 6ab) + (a + 6a - 4a) + (b - 2b) Step 2: Combine like terms. -3ab + (1+6-4)a + (1-2)b -3ab + 3a - b The simplified expression is -3ab + 3a - b. 1.5 -4x^2y - 5xy^2 - 2xy + 3xy - 6xy^2 - x^2y Step 1: Group like terms. (-4x^2y - x^2y) + (-5xy^2 - 6xy^2) + (-2xy + 3xy) Step 2: Combine like terms. (-4-1)x^2y + (-5-6)xy^2 + (-2+3)xy -5x^2y - 11xy^2 + xy The simplified expression is -5x^2y - 11xy^2 + xy. 2. Simplify the following and write your answers in descending powers: 2.1 3a - 5a^2 + 4a + a^2 - 5a Step 1: Group like terms. (-5a^2 + a^2) + (3a + 4a - 5a) Step 2: Combine like terms. (-5+1)a^2 + (3+4-5)a -4a^2 + 2a The simplified expression in descending powers is -4a^2 + 2a. 2.2 4a^2 + 3a - 2 - 4a + a^2 - 3 Step 1: Group like terms. (4a^2 + a^2) + (3a - 4a) + (-2 - 3) Step 2: Combine like terms. (4+1)a^2 + (3-4)a + (-2-3) 5a^2 - a - 5 The simplified expression in descending powers is 5a^2 - a - 5. 2.3 ab + 6a^2 + 5b^2 - 2a^2 - 4ab - b^2 + 3a^2 Step 1: Group like terms. (6a^2 - 2a^2 + 3a^2) + (5b^2 - b^2) + (ab - 4ab) Step 2: Combine like terms. (6-2+3)a^2 + (5-1)b^2 + (1-4)ab 7a^2 + 4b^2 - 3ab Step 3: Arrange in descending powers (typically by the first variable, 'a'). 7a^2 - 3ab + 4b^2 The simplified expression in descending powers is 7a^2 - 3ab + 4b^2. 2.4 6a - 2 + a^2 - a - 5 - 4a^2 + 3a + 4 Step 1: Group like terms. (a^2 - 4a^2) + (6a - a + 3a) + (-2 - 5 + 4) Step 2: Combine like terms. (1-4)a^2 + (6-1+3)a + (-2-5+4) -3a^2 + 8a - 3 The simplified expression in descending powers is -3a^2 + 8a - 3. 2.5 2a^2 + 4a^3 - a^2 - 3a^2 + a + 2a^2 - 6a^3 + a Step 1: Group like terms. (4a^3 - 6a^3) + (2a^2 - a^2 - 3a^2 + 2a^2) + (a + a) Step 2: Combine like terms. (4-6)a^3 + (2-1-3+2)a^2 + (1+1)a -2a^3 + 0a^2 + 2a -2a^3 + 2a The simplified expression in descending powers is -2a^3 + 2a. Send me the next one 📸