$3x(2x + 5) = 3x * 2x + 3x * 5 = 6x^2 + 15x$

$4x(2x^2 - 8x - 2) = 4x * 2x^2 - 4x * 8x - 4x * 2 = 8x^3 - 32x^2 - 8x$

$-2a(a^2 + a - 3) = (-2a) * a^2 + (-2a) * a - (-2a) * 3 = -2a^3 - 2a^2 + 6a$

$5b^2(3b^2 - 7b + 10) = 5b^2 * 3b^2 - 5b^2 * 7b + 5b^2 * 10 = 15b^4 - 35b^3 + 50b^2$

$mn(m^2n - n^3) = mn * m^2n - mn * n^3 = m^3n^2 - mn^4$

$2ab(a^3 - 3a^2b + b^2) = 2ab * a^3 - 2ab * 3a^2b + 2ab * b^2 = 2a^4b - 6a^3b^2 + 2ab^3$

$(4y^3 - 6y + 7) * (-1,2y^3) = 4y^3 * (-1,2y^3) - 6y * (-1,2y^3) + 7 * (-1,2y^3) = -4,8y^6 + 7,2y^4 - 8,4y^3$

$0,4x^2y(3xy^2 - 5xy + 13x^2y^3) = 0,4x^2y * 3xy^2 - 0,4x^2y * 5xy + 0,4x^2y * 13x^2y^3 = 1,2x^3y^3 - 2x^3y^2 + 5,2x^4y^4$

$(2,3a^3b - 1,7b^4 - 3,5b) * (-10a^2b) = 2,3a^3b * (-10a^2b) - 1,7b^4 * (-10a^2b) - 3,5b * (-10a^2b) = -23a^5b^2 + 17a^2b^5 + 35a^2b^2$

$-4pk^3(3p^2k - p + 4k - 2) = (-4pk^3) * 3p^2k - (-4pk^3) * p + (-4pk^3) * 4k - (-4pk^3) * 2 = -12p^3k^4 + 4p^2k^3 - 16pk^4 + 8pk^3$

$\frac{2}{3}mn^2(6m - 1,8n + 9) = \frac{2}{3}mn^2 * 6m - \frac{2}{3}mn^2 * 1,8n + \frac{2}{3}mn^2 * 9 = 4m^2n^2 - 1,2mn^3 + 6mn^2$

$1\frac{1}{7}cd(\frac{7}{8}c^5 - \frac{7}{24}c^2d^7 - \frac{1}{4}d^{10}) = \frac{8}{7}cd * \frac{7}{8}c^5 - \frac{8}{7}cd * \frac{7}{24}c^2d^7 - \frac{8}{7}cd * \frac{1}{4}d^{10} = c^6d - \frac{1}{1} * \frac{1}{3}c^3d^8 - \frac{2}{7}* \frac{1}{1}cd^{11} = c^6d - \frac{1}{3}c^3d^8 - \frac{2}{7}cd^{11}$