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.
ScanSolve AI Answer
Here are the solutions for each part of the problem. Let the two algebraic expressions be: E_1 = 2x^2 - 4x + 6 E_2 = 8x^2 + 4x - 2 a) Find the sum of the two expressions. Step 1: Add the two expressions. E_1 + E_2 = (2x^2 - 4x + 6) + (8x^2 + 4x - 2) Step 2: Combine like terms. E_1 + E_2 = (2x^2 + 8x^2) + (-4x + 4x) + (6 - 2) E_1 + E_2 = 10x^2 + 0x + 4 E_1 + E_2 = 10x^2 + 4 b) Find the difference between the two expressions. Step 1: Subtract the second expression from the first. E_1 - E_2 = (2x^2 - 4x + 6) - (8x^2 + 4x - 2) Step 2: Distribute the negative sign. E_1 - E_2 = 2x^2 - 4x + 6 - 8x^2 - 4x + 2 Step 3: Combine like terms. E_1 - E_2 = (2x^2 - 8x^2) + (-4x - 4x) + (6 + 2) E_1 - E_2 = -6x^2 - 8x + 8 E_1 - E_2 = -6x^2 - 8x + 8 c) If x = 1, find the number value of each expression. Step 1: Substitute x=1 into E_1. E_1 = 2(1)^2 - 4(1) + 6 E_1 = 2(1) - 4 + 6 E_1 = 2 - 4 + 6 E_1 = -2 + 6 E_1 = 4 Step 2: Substitute x=1 into E_2. E_2 = 8(1)^2 + 4(1) - 2 E_2 = 8(1) + 4 - 2 E_2 = 8 + 4 - 2 E_2 = 12 - 2 E_2 = 10 d) If x = -2, what is the number value of the sum of the expressions? Step 1: Use the sum expression from part a), S(x) = 10x^2 + 4. Step 2: Substitute x=-2 into the sum expression. S(-2) = 10(-2)^2 + 4 S(-2) = 10(4) + 4 S(-2) = 40 + 4 S(-2) = 44 e) If x = -3, what is the number value of the difference of the expressions? Step 1: Use the difference expression from part b), D(x) = -6x^2 - 8x + 8. Step 2: Substitute x=-3 into the difference expression. D(-3) = -6(-3)^2 - 8(-3) + 8 D(-3) = -6(9) - (-24) + 8 D(-3) = -54 + 24 + 8 D(-3) = -30 + 8 D(-3) = -22 Send me the next one 📸