1³+2³+2(4)³+(-5)³+(-6)³ solve using suitable identities
To solve the given expression, we can use the identity for the sum of consecutive cubes. The identity states that:
a³ + b³ = (a + b)(a² - ab + b²)
Let's apply this identity step by step:
1³ + 2³ + 2(4)³ + (-5)³ + (-6)³
First, we can simplify the expression by calculating the cubes:
1 + 8 + 2(64) + (-125) + (-216)
Now, let's group the terms:
(1 + 8) + 2(64) + (-125) + (-216)
We can see that (1 + 8) is equal to 9, so substituting it:
9 + 2(64) + (-125) + (-216)
Next, we multiply 2 by 64:
9 + 128 + (-125) + (-216)
Now, we can combine the terms:
9 + 128 - 125 - 216
Simplifying further:
(9 - 125) + (128 - 216)
-116 + (-88)
Finally, adding the terms:
-116 - 88
= -204
Therefore, the value of the given expression is -204.