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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Welcome back yadavyogendra88080 — missed you this week. Here are the solutions to the addition problems: 1. Step 1: Write the expression for addition. 8ab + (-5ab) + 3ab + (-ab) Step 2: Combine the coefficients of the like terms. (8 - 5 + 3 - 1)ab = (3 + 3 - 1)ab = (6 - 1)ab = 5ab The sum is 5ab. 2. Step 1: Write the expression for addition. 7x + (-3x) + 5x + (-x) + (-2x) Step 2: Combine the coefficients of the like terms. (7 - 3 + 5 - 1 - 2)x = (4 + 5 - 1 - 2)x = (9 - 1 - 2)x = (8 - 2)x = 6x The sum is 6x. 3. Step 1: Write the expression for addition, grouping like terms. (3a - 4b + 4c) + (2a + 3b - 8c) + (a - 6b + c) = (3a + 2a + a) + (-4b + 3b - 6b) + (4c - 8c + c) Step 2: Combine the coefficients for each variable. = (3 + 2 + 1)a + (-4 + 3 - 6)b + (4 - 8 + 1)c = 6a + (-1 - 6)b + (-4 + 1)c = 6a - 7b - 3c The sum is 6a - 7b - 3c. 4. Step 1: Write the expression for addition, grouping like terms. (5x - 8y + 2z) + (3z - 4y - 2x) + (6y - z - x) + (3x - 2z - 3y) = (5x - 2x - x + 3x) + (-8y - 4y + 6y - 3y) + (2z + 3z - z - 2z) Step 2: Combine the coefficients for each variable. = (5 - 2 - 1 + 3)x + (-8 - 4 + 6 - 3)y + (2 + 3 - 1 - 2)z = (3 - 1 + 3)x + (-12 + 6 - 3)y + (5 - 1 - 2)z = (2 + 3)x + (-6 - 3)y + (4 - 2)z = 5x - 9y + 2z The sum is 5x - 9y + 2z. 5. Step 1: Write the expression for addition, grouping like terms. (6ax - 2by + 3cz) + (6by - 11ax - cz) + (10cz - 2ax - 3by) = (6ax - 11ax - 2ax) + (-2by + 6by - 3by) + (3cz - cz + 10cz) Step 2: Combine the coefficients for each variable. = (6 - 11 - 2)ax + (-2 + 6 - 3)by + (3 - 1 + 10)cz = (-5 - 2)ax + (4 - 3)by + (2 + 10)cz = -7ax + by + 12cz The sum is -7ax + by + 12cz. 6. Step 1: Write the expression for addition, grouping like terms by degree. (2x^3 - 9x^2 + 8) + (3x^2 - 6x - 5) + (7x^3 - 10x + 1) + (3 + 2x - 5x^2 - 4x^3) = (2x^3 + 7x^3 - 4x^3) + (-9x^2 + 3x^2 - 5x^2) + (-6x - 10x + 2x) + (8 - 5 + 1 + 3) Step 2: Combine the coefficients for each term. = (2 + 7 - 4)x^3 + (-9 + 3 - 5)x^2 + (-6 - 10 + 2)x + (8 - 5 + 1 + 3) = (9 - 4)x^3 + (-6 - 5)x^2 + (-16 + 2)x + (3 + 1 + 3) = 5x^3 - 11x^2 - 14x + 7 The sum is 5x^3 - 11x^2 - 14x + 7. 7. Step 1: Write the expression for addition, grouping like terms. (6p + 4q - r + 3) + (2r - 5p - 6) + (11q - 7p + 2r - 1) + (2q - 3r + 4) = (6p - 5p - 7p) + (4q + 11q + 2q) + (-r + 2r + 2r - 3r) + (3 - 6 - 1 + 4) Step 2: Combine the coefficients for each variable and constant. = (6 - 5 - 7)p + (4 + 11 + 2)q + (-1 + 2 + 2 - 3)r + (3 - 6 - 1 + 4) = (1 - 7)p + (15 + 2)q + (1 + 2 - 3)r + (-3 - 1 + 4) = -6p + 17q + (3 - 3)r + (-4 + 4) = -6p + 17q + 0r + 0 = -6p + 17q The sum is -6p + 17q. 8. Step 1: Write the expression for addition, grouping like terms. (4x^2 - 7xy + 4y^2 - 3) + (5 + 6y^2 - 8xy + x^2) + (6 - 2xy + 2x^2 - 5y^2) = (4x^2 + x^2 + 2x^2) + (-7xy - 8xy - 2xy) + (4y^2 + 6y^2 - 5y^2) + (-3 + 5 + 6) Step 2: Combine the coefficients for each term. = (4 + 1 + 2)x^2 + (-7 - 8 - 2)xy + (4 + 6 - 5)y^2 + (-3 + 5 + 6) = 7x^2 + (-15 - 2)xy + (10 - 5)y^2 + (2 + 6) = 7x^2 - 17xy + 5y^2 + 8 The sum is 7x^2 - 17xy + 5y^2 + 8. Drop the next question 📸