Question

using suitable identities find the value of (-16)^3+(7)^3+(9)^3
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Answer 1

Answer:

Use a suitable identity to get each of the following products: (i) \left(x+3 ight)\left(x+3 ight) (ii) \left(2y+5 ight)\left(2y+5 ight) (iii) \left(2a-7 ..

Answer 2

Step-by-step explanation:

Given :-

(-16)^3+(7)^3+(9)^3

To find:-

Using suitable identities find the value of (-16)^3+(7)^3+(9)^3 ?

Solution:-

Given that

(-16)^3+(7)^3+(9)^3

It is in the form of a^3 + b^3 + c^3

Where ,

a = -16

b= 7

c = 9

and

a + b + c

=> (-16)+(7)+(9)

=> (-16)+(16)

=> -16+16

=> 0

We have ,

a + b + c = 0

We know that

If a+ b + c = 0 then a^3 + b^3 + c^3 = 3abc

Now

We have

(-16)+(7)+(9) = 0 then (-16)^3 + (7)^3 + (9)^3

=> 3(-16)(7)(9)

=> - 3024

Answer:-

The value of (-16)^3 + (7)^3 + (9)^3 is -3024

Check:-

(-16)^3 + (7)^3 + (9)^3

=> (-4096) + (343)+(729)

=> (-4096)+(1072)

=> -4096+1072

=> - 3024

Verified the given relation.

Used Identity:-

If a+b+c=0 then a^3 + b^3 + c^3 = 3abc

Additional information:-

Some more Identities:-

• (a+b)^2=a^2+2ab+b^2

• (a-b)^2=a^2-2ab+b^2

• (a+b)(a-b)=a^2-b^2

• (x+a)(x+b)=x^2+(a+b)x+ab

• (a+b)^3 =a^3+3a^2b+3ab^2+b^3

• (a+b)^3 =a^3+3ab(a+b)+b^3

• (a-b)^3 =a^3-3a^2b+3ab^2-b^3
• (a-b)^3 =a^3-3ab(a-b)-b^3

• (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca

• a^3+b^3=(a+b)(a^2-ab+b^2)

• a^3-b^3=(a-b)(a^2+ab+b^2)