Đáp án:
$12. 64m^{3} - 240m^{2}n + 300mn^{2} - 125n^{3}$
$13. 216z^{3} + 324z^{2}t + 162zt^{2} + 27t^{3}$
$14. 64x^{3} - 288x^{2}y + 432xy^{2} - 216y^{3}$
$15. 1000a^{3} + 2100a^{2}b + 1470ab^{2} + 343b^{3}$
$16. \frac{1}{8}x^{3} + \frac{9}{4}x^{2}y + \frac{27}{2}xy^{2} + 27y^{3}$
Giải thích các bước giải:
$12. ( 4m - 5n )^{3}$
$= (4m)^{3} - 3.4m.5n.( 4m - 5n ) - (5n)^{3}$
$= 64m^{3} - 60mn( 4m - 5n ) - 125n^{3}$
$= 64m^{3} - 240m^{2}n + 300mn^{2} - 125n^{3}$
$13. ( 6z + 3t )^{3}$
$= (6z)^{3} + 3.6z.3t.( 6z + 3t ) + (3t)^{3}$
$= 216z^{3} + 54zt( 6z + 3t ) + 27t^{3}$
$= 216z^{3} + 324z^{2}t + 162zt^{2} + 27t^{3}$
$14. ( 4x - 6y )^{3}$
$= (4x)^{3} - 3.4x.6y.( 4x - 6y ) - (6y)^{3}$
$= 64x^{3} - 72xy( 4x - 6y ) - 216y^{3}$
$= 64x^{3} - 288x^{2}y + 432xy^{2} - 216y^{3}$
$15. ( 10a + 7b )^{3}$
$= (10a)^{3} + 3.10a.7b.( 10a + 7b ) + (7b)^{3}$
$= 1000a^{3} + 210ab( 10a + 7b ) + 343b^{3}$
$= 1000a^{3} + 2100a^{2}b + 1470ab^{2} + 343b^{3}$
$16. ( \frac{1}{2}x + 3y )^{3}$
$= (\frac{1}{2}x)^{3} + 3.\frac{1}{2}x.3y.( \frac{1}{2}x + 3y ) + (3y)^{3}$
$= \frac{1}{8}x^{3} + \frac{9}{2}xy( \frac{1}{2}x + 3y ) + 27y^{3}$
$= \frac{1}{8}x^{3} + \frac{9}{4}x^{2}y + \frac{27}{2}xy^{2} + 27y^{3}$