в) y8–1=(y4 – 1)(y4 + 1) = (y2 – 1)(y2 + 1)(y4 + 1)=(y–1)(y+1)(y2 + 1)(y4 + 1); г) x4 – z4 = (x2 – z2)(x2 + z2) = (x – z)(x + z)(x2 + z2). № 646 а) 4m3 – 4n3 = 4(m3 – n3) = 4(m – n)(m2 + mn + n2); б) 13a3 + 13b3 = 13(a3 + b3) = 13(a + b)(a2 – ab + b2); в) 15c3 + 15d3 = 15(c3 + d3) = 15(c + d)(c2 – cd + d2); г) 21s3 – 21t3 = 21(s3 – t3) = 21(s – t)(s2 + st + t2). № 647 а) 6x5y – 24xy3 = 6xy(x4 – 4y2) = 6xy(x2 – 2y)(x2 + 2y); б) 3a4b2 + 24ab5 = 3ab2(a3 + 8b3) = 3ab(a + 2b)(a2 – 2ab + 4b2; в) 0,3y2 – 2,7y6 = 0,3y2(1 – 9y4) = 0,3y2(1 – 3y2)(1 + 3y2); г) 0,1x4y – 2,7xy4 = 0,1xy(x3 – 27y3) = 0,1xy(x – 3y)(x2 + 3xy + 9y2). № 648 а) (m + 3)3 – 8 = (m + 3 – 2)((m + 3)2 + 2(m + 3) + 4) = = (m + 1)(m2 + 6m + 9 + 2m + 6 + 4) = (m + 1)(m2 + 8m + 19); б) (c–1)3+27 = (c – 1 + 3)(c2 – 2c + 1 – 3c + 3 + 9) = (c + 2)(c2 – 5c + 12); в) (a–12)3–125 = (a–12–5)(a2–24a+144+5a–60+25)=(a – 17)(a2–19a+109); г) (b+4)3+64=(b+4+4)(b2+8b+16+4b+16+16) = (b + 8)(b2 + 12b + 48). № 649 а) (x2 + 1)2 – 4x2 = (x2 + 1 – 2x)(x2 + 1 + 2x) = (x – 1)2(x + 1)2; б) (y2 + 2y)2 – 1 = (y2 + 2y – 1)(y2 + 2t + 1) = (y2 + 2y – 1)(y + 1)2; в) 81 – (c2 + 6c)2 = (9 – c2 – 6c)(9 + c2 + 6c) = (9 – c2 – 6c)(c + 3)2; г) 16m2 – (m – n)2 = (4m – m + n)(4m + m – n) = (3m + n)(5m – n). № 650 а) (a2 + 2ab + b2) – c2 = (a + b)2 – c2 = (a + b – c)(a + b +c); б) 16 – (x2 – 2xy + y2) = 16 – (x – y)2 = (4 – x + y)(4 + x – y); в) 1 – m2 – 2mn – n2 = 1 – (m + n)2 = (1 – m – n)( 1 + m + n); г) 4 – p2 – 2pq – q2 = 4 – (p + q)2 = (2 – p – q)(2 + p + q). № 651 а) x2 – 2xc + c2 – d2 = (x – c)2 – d2 = (x – c – d)(x – c + d); б) a2 + 2a – b2 + 1 = (a + 1)2 – b2 = (a + 1 – b)(a + 1 + b); в) c2 – d2 + 6c + 9 = (c + 3)2 – d2 = (c + 3 – d)(c + 3 + d); г) r2 – s2 – 10s – 25 = r2 – (s + 5)2 = (r – s – 5)(r + s + 5). № 652 а) x2 + 2xy – m2 + y2 = (x + y)2 – m2 = (x = y – m)(x = y + m); б) c2 – a2 + 2ab – b2 = c2 – (a – b)2 = (c – a + b)(c + a – b); в) m2 – n2 – 8m + 16 = (m – 4)2 – n2 = (m – 4 – n)(m – 4 + n); г) 9 – p2 + q2 – 6q = (q – 3)2 – p2 = (q – 3 – p)(q – 3 + p).
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