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 simplifications for the expressions: d) Step 1: Use the FOIL method to expand the product of the two binomials. (sqrt(5)+2)(sqrt(5)-1) = sqrt(5) × sqrt(5) + sqrt(5) × (-1) + 2 × sqrt(5) + 2 × (-1) Step 2: Simplify each term. 5 - sqrt(5) + 2sqrt(5) - 2 Step 3: Combine like terms. (5-2) + (-1+2)sqrt(5) 3 + sqrt(5) 3 + sqrt(5) h) Step 1: Rewrite the division as a fraction. 7sqrt(30) ÷ sqrt(2) = 7sqrt(30)sqrt(2) Step 2: Separate the coefficient and the surds. 7 × sqrt(30)sqrt(2) Step 3: Simplify the surds. 7 × sqrt((30)/(2)) 7 × sqrt(15) 7sqrt(15) 7sqrt(15) What's next?