Question

Find the value of 64x3 - 125z3, if 4x - 5z=16 and xz=12.

Answer 1

$using \: {a}^{3} - {b}^{3} = {(a - b)}^{3} + 3 ab(a - b) \\ 64 {x}^{3} - 125 {z}^{3} = {(4x)}^{3} - {(5z)}^{3} = \\ {(4x - 5z)}^{3} + 3 \times 4x \times 5z(4x - 5z) \\ = {16}^{3} + 3 \times 4 \times 5 \times 12 \times 16 = 15616 \:$

Answer 2

Answer:

Step-by-step explanation:

x3-y3= (x-y)(x2+xy+y2)

(4x)3-(5y)3=(4x-5y)(16x2 + 20xy +25y2)

=(16)(16x2 +25y2 + 240)

(4x-5y)2= 16x2 - 40xy +25 y2

(16)2= 16x2 + 25y2 -40(12)

256+ 480= 16x2 +25y2

=736

64x3 - 125y3= 16(736+240)

                      =16(976)

                     =15616