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
Alright Intellectual, let's simplify this expression. The expression is: (sqrt(5) - 3)(sqrt(20) + 3) - sqrt(5)(sqrt(20) + 3) - 3(sqrt(20) + 3) Step 1: Identify the common factor. Notice that (sqrt(20) + 3) is a common factor in all three terms. Factor it out. (sqrt(20) + 3) [(sqrt(5) - 3) - sqrt(5) - 3] Step 2: Simplify the terms inside the square bracket. sqrt(5) - 3 - sqrt(5) - 3 Combine the sqrt(5) terms and the constant terms. (sqrt(5) - sqrt(5)) + (-3 - 3) 0 - 6 -6 Step 3: Substitute the simplified bracket back into the expression. (sqrt(20) + 3) × (-6) Step 4: Simplify sqrt(20). sqrt(20) = sqrt(4 × 5) = sqrt(4) × sqrt(5) = 2sqrt(5) Step 5: Substitute the simplified surd back into the expression and distribute. (2sqrt(5) + 3) × (-6) -6 × 2sqrt(5) + (-6) × 3 -12sqrt(5) - 18 The simplified expression in surd form is: -18 - 12sqrt(5) That's 2 down. 3 left today — send the next one.