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
Huu hapa ni ufumbuzi wa maswali yako: 5. Rahisisha usemi. (a - 4ab + a^2 - 4b)/(4b^2 - a^2b - ab - 4ab^2) Step 1: Rahisisha nambari (numerator) kwa kuweka vigezo pamoja. a - 4ab + a^2 - 4b Panga upya vigezo: a^2 + a - 4ab - 4b Weka vigezo pamoja na toa vigezo vya kawaida: a(a+1) - 4b(a+1) Toa (a+1) kama kigezo cha kawaida: (a+1)(a-4b) Step 2: Rahisisha kinyume (denominator) kwa kuweka vigezo pamoja. 4b^2 - a^2b - ab - 4ab^2 Toa b kama kigezo cha kawaida kutoka kwa vigezo vyote: b(4b - a^2 - a - 4ab) Panga upya vigezo ndani ya mabano: b(-a^2 - a + 4b - 4ab) Weka vigezo pamoja ndani ya mabano: b[-a(a+1) + 4b(1-a)] Kwa kuwa hakuna kigezo cha kawaida kati ya nambari (a+1)(a-4b) na kinyume b[-a(a+1) + 4b(1-a)], usemi hauwezi kurahisishwa zaidi kwa kufuta vigezo. Usemi uliorahisishwa ni: ((a+1)(a-4b))/(b[-a(a+1) + 4b(1-a)]) 6. Kutokana na a = -2, b = 5 na c = -1, tathmini. (4a^3 + 5b - c)/(1)3(c^2 - a^2) Step 1: Badilisha thamani za a, b, c kwenye nambari (numerator). 4a^3 + 5b - c = 4(-2)^3 + 5(5) - (-1) = 4(-8) + 25 + 1 = -32 + 25 + 1 = -7 + 1 = -6 Step 2: Badilisha thamani za a, c kwenye kinyume (denominator). (1)/(3)(c^2 - a^2) = (1)/(3)((-1)^2 - (-2)^2) = (1)/(3)(1 - 4) = (1)/(3)(-3) = -1 Step 3: Gawanya nambari kwa kinyume. (-6)/(-1) = 6 Thamani ya usemi ni 6. Drop the next question.