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
Hey Ðƴŋâmïč̣, good to see you again. Step 1: Expand the terms in the numerator. The numerator is 5x^2(12x^2+6x) - (4x^3+3x^2) · 10. First part: 5x^2(12x^2+6x) = (5x^2 · 12x^2) + (5x^2 · 6x) = 60x^2+2 + 30x^2+1 = 60x^4 + 30x^3 Second part: (4x^3+3x^2) · 10 = (4x^3 · 10) + (3x^2 · 10) = 40x^3 + 30x^2 Now substitute these back into the numerator: (60x^4 + 30x^3) - (40x^3 + 30x^2) Step 2: Simplify the numerator by combining like terms. 60x^4 + 30x^3 - 40x^3 - 30x^2 60x^4 + (30x^3 - 40x^3) - 30x^2 60x^4 - 10x^3 - 30x^2 Step 3: Expand the denominator. The denominator is (5x^2)^2. (5x^2)^2 = 5^2 · (x^2)^2 = 25x^2 · 2 = 25x^4 Step 4: Divide the simplified numerator by the simplified denominator. The expression becomes: (60x^4 - 10x^3 - 30x^2)/(25x^4) Divide each term in the numerator by the denominator: (60x^4)/(25x^4) - (10x^3)/(25x^4) - (30x^2)/(25x^4) Simplify each fraction: (60)/(25) - (10)/(25x) - (30)/(25x^2) Reduce the numerical coefficients: (12 · 5)/(5 · 5) - (2 · 5)/(5 · 5x) - (6 · 5)/(5 · 5x^2) (12)/(5) - (2)/(5x) - (6)/(5x^2) The simplified expression is: (12)/(5) - (2)/(5x) - (6)/(5x^2) Send me the next one 📸