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 the problems. b) Step 1: Distribute 3x into the first parenthesis and x into the second parenthesis. 3x(x - 2y - 5z) + x(x + 6y) 3x · x - 3x · 2y - 3x · 5z + x · x + x · 6y 3x^2 - 6xy - 15xz + x^2 + 6xy Step 2: Identify and combine like terms. (3x^2 + x^2) + (-6xy + 6xy) - 15xz 4x^2 + 0 - 15xz 4x^2 - 15xz The expanded and simplified expression is 4x^2 - 15xz. 4. a) Step 1: Expand the expression (a + 4)(3a + 7) using the FOIL method (First, Outer, Inner, Last). (a)(3a) + (a)(7) + (4)(3a) + (4)(7) 3a^2 + 7a + 12a + 28 Step 2: Combine the like terms. 3a^2 + (7a + 12a) + 28 3a^2 + 19a + 28 The expanded and simplified expression is 3a^2 + 19a + 28. b) Step 1: Expand the expression (x + 10)(x - 10) using the FOIL method. This is also a difference of squares pattern (A+B)(A-B) = A^2 - B^2. (x)(x) + (x)(-10) + (10)(x) + (10)(-10) x^2 - 10x + 10x - 100 Step 2: Combine the like terms. x^2 + (-10x + 10x) - 100 x^2 + 0 - 100 x^2 - 100 The expanded and simplified expression is x^2 - 100. c) Step 1: Expand the expression (2x - 5y)(3x - 4y) using the FOIL method. (2x)(3x) + (2x)(-4y) + (-5y)(3x) + (-5y)(-4y) 6x^2 - 8xy - 15xy + 20y^2 Step 2: Combine the like terms. 6x^2 + (-8xy - 15xy) + 20y^2 6x^2 - 23xy + 20y^2 The expanded and simplified expression is 6x^2 - 23xy + 20y^2. That's 2 down. 3 left today — send the next one.