Question

8. Use property to evaluate : (i) 133 + (-8) + (-5)3 (ii) 73 +33 + (-10)3 (iii) 93 - 53 - 43 (iv) 383 + (-26)3 + (-12)3​

Answer 1

2197-512-125

=2197-637

=2560

(II)

3(7)(3)(-10)

=-630

(III)

93+(−5)3+(−4)3

We know that

a3+b3+c3−3abc=(a+b+c)(a2+b2+c2−ab−ac−bc)

If (a+b+c)=0, then.

a3+b3+c3=3abc

Here,

a=9

b=−5

c=−4

and a+b+c=9−5−4=0

Thus,

93+(−5)3+(−4)3

=3(9)(−5)(−4)

=540

(IV)

Given, 383+(−26)3+(−12)3

We know that

a3+b3+c3−3abc=(a+b+c)(a2+b2+c2−ab−ac−bc)

If (a+b+c)=0, then. a3+b3+c3=3abc

Here,

a=38

b=−26

c=−12

∴a+b+c=38−26−12=0

Thus,

383+(−26)3+(−12)3

=3(38)(−26)(−12)

=35568

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Answer 2

Step-by-step explanation:

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