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.
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Ili kugawa usemi 9x^3y^2 - 4xy^4, tutatafuta kigezo cha kawaida kikubwa (GCF) kwanza, kisha tutatumia tofauti ya miraba. Step 1: Tafuta kigezo cha kawaida kikubwa (GCF) cha maneno yote mawili. Maneno ni 9x^3y^2 na 4xy^4. • Kwa nambari (coefficients): GCF ya 9 na 4 ni 1. • Kwa x: GCF ya x^3 na x ni x. • Kwa y: GCF ya y^2 na y^4 ni y^2. Hivyo, GCF ya usemi mzima ni xy^2. Step 2: Toa GCF kutoka kwa kila neno. 9x^3y^2 - 4xy^4 = xy^2(9x^2 - 4y^2) Step 3: Angalia usemi ndani ya mabano. Usemi 9x^2 - 4y^2 ni tofauti ya miraba, ambayo inaweza kugawanywa kwa kutumia fomula a^2 - b^2 = (a-b)(a+b). Hapa, a^2 = 9x^2 a = sqrt(9x^2) = 3x. Na b^2 = 4y^2 b = sqrt(4y^2) = 2y. Kwa hiyo, 9x^2 - 4y^2 = (3x - 2y)(3x + 2y). Step 4: Unganisha GCF na matokeo ya ugawaji wa tofauti ya miraba. xy^2(9x^2 - 4y^2) = xy^2(3x - 2y)(3x + 2y) Usemi uliogawanywa kikamilifu ni: xy^2(3x - 2y)(3x + 2y) That's 2 down. 3 left today — send the next one.