Відповіді до вправ 501 - 600 » 559

559. Розкладіть многочлен на множники: 1) a3 – b6 = a3 – (b2)3 = (a – b2)(a2 + ab2 + b4); 2) t12 + c9 = (t4)3 + (c3)3 = (t4 + c3)((t8 – t4c3 + c6); 3) p18 + m24 = (p6)3 + (m8)3 = (p6 + m8)((p6)2 –р6m8 + (m8)2)= (p6 + m8)(p12 – p6m8 + m16); 4) –c3 + m15 =(m5)3 – c3 = (m5 – c)((m5)2 + m5c + c2) =(m5 – c)(m10 + m5c + c2); 5) –1/8 – a24 = –((1/2)3 + (a8)3) = –(1/2 + a8)(( 1/2)2 – 1/2a8 + (a8)2) = –(1/2 + a8)( 1/4 – 1/2a8 + a16); 6) –c99 – d60 = –((c33)3 + (d20))3 = –(c33 + d20)((c33)2 – c33d20 + (d20)2) = –(c33 + d20)(c66 – c33d20 + d40); 7) x3y3 + 1 = (xy + 1)(x2y2 – xy + 1); 8) 27 – a3b9 = 33 – (ab3)3 = (3 – ab3)(32 + 3 ∙ ab3 + (ab3)2) = (3 – – ab3) ∙ (9 + 3аb3 + a2b6); 9) x6y12 + m27 = (x2y4)3 + (m9)3 = (x2y4 + m9)(x4y8 – x2y4m9 +m18); 10) 64m6p21 – 125x3 = (4m2p7)3 – (5x)3 = (4m2р7 – 5х)(16m4p14 – 4m2p7 ∙ 5x + 25x2) = (4m2p7 – 5x)(16m4p14 – 20m2p7x + 25x2); 11) 1/27c24m18 + 27t9 = (1/3c8m6)3 + (3t3)3 = (1/3c8m6 + 3t3)( 1/9c16m12 – – c8m6t3 + 9t6); 12) 343a18b33 – 0,001c36 = (7a6b11)3 – (0,1c12)3 = (7a6b11 – 0,1c12) ∙ (49a12b22 – 0,7a6b11c12 + 0,01c24).