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
Morning — let's get this done. a) Step 1: Expand the first term (2x + 3)(x - 4). (2x + 3)(x - 4) = 2x(x) + 2x(-4) + 3(x) + 3(-4) = 2x^2 - 8x + 3x - 12 = 2x^2 - 5x - 12 Step 2: Expand the second term (x + 1)^2. (x + 1)^2 = x^2 + 2(x)(1) + 1^2 = x^2 + 2x + 1 Step 3: Add the expanded terms and combine like terms. (2x^2 - 5x - 12) + (x^2 + 2x + 1) = (2x^2 + x^2) + (-5x + 2x) + (-12 + 1) = 3x^2 - 3x - 11 The simplified expression is: 3x^2 - 3x - 11 b) Step 1: Divide the coefficients and use the exponent rule (x^m)/(x^n) = x^m-n. (24x^6)/(4x^2) = (24)/(4) · x^6-2 = 6x^4 The simplified expression is: 6x^4 c) Step 1: Use the logarithm property n a = a^n for the first term. 22 = (2^2) = 4 Step 2: Substitute this back into the expression. 4 + 5 - 4 Step 3: Use the logarithm property a + b = (ab) for the first two terms. (4 × 5) - 4 = 20 - 4 Step 4: Use the logarithm property a - b = ((a)/(b)). ((20)/(4)) = 5 The simplified expression is: log5 d) Step 1: Factor out the common term from the numerator. (4a+8)/(2) = (4(a+2))/(2) Step 2: Simplify the fraction. (4(a+2))/(2) = 2(a+2) = 2a+4 The simplified expression is: 2a+4 e) Step 1: Distribute 3x into (x - 2). 3x(x - 2) = 3x^2 - 6x Step 2: Distribute -2x into (x + 4). -2x(x + 4) = -2x^2 - 8x Step 3: Combine the results and collect like terms. (3x^2 - 6x) - (2x^2 + 8x) = 3x^2 - 6x - 2x^2 - 8x = (3x^2 - 2x^2) + (-6x - 8x) = x^2 - 14x The simplified expression is: x^2 - 14x f) Step 1: Use the exponent rule a^-n = (1)/(a^n). 8^-(2)/(3) = (1)/(8^2)3 Step 2: Use the exponent rule a^(m)/(n) = ([n]a)^m. 8^(2)/(3) = ([3]8)^2 Step 3: Calculate the cube root of 8. [3]8 = 2 Step 4: Square the result. 2^2 = 4 Step 5: Substitute back into the fraction. (1)/(4) The simplified expression is: (1)/(4) Got more? Send 'em 📸