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 to the problems: 1 Simplify 3(x+3) - 2x(x-1). Step 1: Expand the terms by distributing. 3(x+3) = 3x + 9 -2x(x-1) = -2x^2 + 2x Step 2: Combine the expanded terms. 3x + 9 - 2x^2 + 2x Step 3: Group and combine like terms. -2x^2 + (3x + 2x) + 9 -2x^2 + 5x + 9 The simplified expression is -2x^2 + 5x + 9. 2 Evaluate 4^(1)/(2) × 4. Step 1: Evaluate the fractional exponent. 4^(1)/(2) is equivalent to sqrt(4). sqrt(4) = 2 Step 2: Perform the multiplication. 2 × 4 = 8 The evaluated expression is 8. 3 Factorise completely 3a - c - 3ab + bc. Step 1: Rearrange the terms to group common factors. 3a - 3ab - c + bc Step 2: Factor out common terms from each pair of terms. From the first pair (3a - 3ab), factor out 3a: 3a(1 - b) From the second pair (-c + bc), factor out -c: -c(1 - b) Step 3: Factor out the common binomial factor (1 - b). (1 - b)(3a - c) The completely factorised expression is (1 - b)(3a - c). 3 done, 2 left today. You're making progress.