Without actual calculating the cube the value of (28)^3 +(-15)^3 +(-13)^3 is
(a) 16380
(b)-16380
(c)15380
(d)-15380
Hint:
(13+15)^3 = 13^3 + 3*13^2*15 + 3*13*15^2 + 15^3
using a^3- b^3 = (a-b)(a^2 + ab + b^2)
(28)^3 +(-15)^3 +(-13)^3
= (28 - 15)(28^2 + 28(15) + 15^2) - 13^3
= 13[ 28^2 + 28(15) + 15^2 - 13^2]
= don't know how to avoid doing an actual calculation
To find the value of (28)^3 + (-15)^3 + (-13)^3 without actually calculating the cube, you can use the property:
(a)^3 + (b)^3 + (c)^3 = (a + b + c)(a^2 - ab + b^2) - 3abc
Let's substitute the given values into this formula:
(a) = 28, (b) = -15, (c) = -13
Plugging in these values, we get:
(28)^3 + (-15)^3 + (-13)^3 = (28 + (-15) + (-13))((28)^2 - (28)(-15) + (-15)^2) - 3(28)(-15)(-13)
Simplifying further:
= (28 - 15 - 13)((28)^2 + (28)(15) + (15)^2) - 3(28)(-15)(-13)
= (0)((28)^2 + (28)(15) + (15)^2) - 3(28)(-15)(-13)
Since the first term with (28 - 15 - 13) is 0, we only need to calculate the last term:
= - 3(28)(-15)(-13)
Now, we can calculate the value:
= -3(28)(15)(13)
= -3(5460)
= -16380
Therefore, the answer is (b) -16380.