Question

Without actually calculation cubes find the value of following
1) minus 10 whole cube + 7 Cube + 3 Cube

Answer 1

( - 10)³ + 7³ + 3³ = - 630

Given :

( - 10)³ + 7³ + 3³

To find :

The value of the expression

Formula :

If a + b + c = 0 then a³ + b³ + c³ = 3abc

Solution :

Step 1 of 2 :

Find the value of ( - 10) + 7 + 3

Let a = - 10 , b = 7 , c = 3

Then we have

a + b + c

= - 10 + 7 + 3

= 0

Step 2 of 2 :

Find the value of the expression

We know that if a + b + c = 0 then a³ + b³ + c³ = 3abc

Thus we get

( - 10)³ + 7³ + 3³

= a³ + b³ + c³

= 3abc

= 3 × ( - 10 ) × 7 × 3

= - 630

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Answer 2

Given,

(-10)³+7³+3³

To find,

The value of (-10)³+7³+3³ without calculating the values using cubes.

Solution,

The value of (-10)³+7³+3³ without calculating the values using cubes will be -630.

We can easily solve this problem by following the given steps.

We know the identity, a³+b³+c³-3abc = (a+b+c) (a²+b²+c²-ab-bc-ca)

Using this identity, if (a+b+c) = 0, then

a³+b³+c³-3abc = 0

a³+b³+c³ = 3abc

In the given case,

(-10+7+3) = 0

So, (a+b+c) is 0 where a = -10, b= 7 and c = 3.

Therefore, we have

a³+b³+c³ = 3abc

(-10)³+7³+3³ = 3 × (-10) × 7 × 3

(-10)³+7³+3³ = 3 × (-70) ×3

(-10)³+7³+3³ = (-70) × 9

(-10)³+7³+3³ = -630

Hence, the value of (-10)³+7³+3³ without calculating the values using cubes is -630.

[More to know: we have around eight major identities to solve the questions straightforwardly. For example, two of the identities are (a+b)² = a²+b²+2ab and a²-b² = (a+b) (a-b).]