Упростите выражение:
а) $(3p - 10q)(100q^2 + 30pq + 9p^2)$;
б) $(7m + 2n)(4n^2 - 14mn + 49m^2)$;
в) $(ab - 3)(a^2b^2 + 3ab + 9)$;
г) $(km - n^2)(k^2m^2 + kmn^2 + n^4)$;
д) $(4y^2 - xy + \frac{1}{4}x^2)(\frac{1}{2}x + 2y)$;
е) $(1,21q^2 + 0,22pq + 0,04p^2)(0,2p - 1,1q)$;
ж) $(\frac{1}{9}m^4 + m^2nk + 9n^2k^2)(\frac{1}{3}m^2 - 3nk)$;
з) $(1\frac{1}{2}a^3 - 0,5b^2)(2\frac{1}{4}a^6 + \frac{3}{4}a^3b^2 + 0,25b^4)$.
$(3p - 10q)(100q^2 + 30pq + 9p^2) = (3p - 10q)(9p^2 + 30pq + 100q^2) = (3p)^3 - (10q)^3 = 27p^3 - 1000q^3$
$(7m + 2n)(4n^2 - 14mn + 49m^2) = (2n + 7m)(4n^2 - 14mn + 49m^2) = (2n)^3 + (7m)^3 = 8n^3 + 343m^3$
$(ab - 3)(a^2b^2 + 3ab + 9) = (ab)^3 - 3^3 = a^3b^3 - 27$
$(km - n^2)(k^2m^2 + kmn^2 + n^4) = (km)^3 - (n^2)^3 = k^3m^3 - n^6$
$(4y^2 - xy + \frac{1}{4}x^2)(\frac{1}{2}x + 2y) = (2y + \frac{1}{2}x)(4y^2 - xy + \frac{1}{4}x^2) = (2y)^3 + (\frac{1}{2}x)^3 = 8y^3 + \frac{1}{8}x^3$
$(1,21q^2 + 0,22pq + 0,04p^2)(0,2p - 1,1q) = (0,2p - 1,1q)(0,04p^2 + 0,22pq + 1,21q^2) = (0,2p)^3 - (1,1q)^3 = 0,008p^3 - 1,331q^3$
$(\frac{1}{9}m^4 + m^2nk + 9n^2k^2)(\frac{1}{3}m^2 - 3nk) = (\frac{1}{3}m^2)^3 - (3nk)^3 = \frac{1}{27}m^6 - 27n^3k^3$
$(1\frac{1}{2}a^3 - 0,5b^2)(2\frac{1}{4}a^6 + \frac{3}{4}a^3b^2 + 0,25b^4) = (\frac{3}{2}a^3)^3 - (0,5b^2)^3 = \frac{27}{8}a^9 - 0,125b^6 = 3\frac{3}{8}a^9 - 0,125b^6$
Пожауйста, оцените решение
