simplify (a+3)³+(a-3)³
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Step-by-step explanation:
Given:-
(a+3)^3+(a-3)^3
To find:-
Simplify (a+3)^3+(a-3)^3
Solution:-
Method-1:-
Given expression is (a+3)^3+(a-3)^3
(a+3)^3 is in the form of (a+b)^3
Where a = a and b=3
We know that
(a+b)^3=a^3+3a^2b+3ab^2+b^3
=>(a+3)^3
=>a^3+3a^2(3)+3a(3)^2+3^3
=>a^3+9a^2+27a+27
and
(a-3)^3 is in the form of (a-b)^3
Where a = a and b=3
We know that
(a-b)^3=a^3-3a^2b+3ab^2-b^3
=>(a-3)^3
=>a^33a^2(3)+3a(3)^2-3^3
=>a^3-9a^2+27a-27
Now,
(a+3)^3+(a-3)^3
=> a^3+9a^2+27a+27+a^3-9a^2+27a-27
=>(a^3+a^3)+(9a^2-9a^2)+(27a+27a)+(27-27)
=>2a^3+0+54a+0
=>2a^3+54a
Method-2:-
Given expression is (a+3)^3+(a-3)^3
It is in the form of (a+b)^3+(a-b)^3
Where a = a and b=3
we know that
(a+b)^3+(a-b)^3 = 2a^3+6ab^2
(a+3)^3+(a-3)^3
=> 2a^3+6(a)(3^2)
=>2a^3+6(a)(9)
=>2a^3+54a
Answer:-
(a+3)^3+(a-3)^3 = 2a^3+54a
Used formulae:-
- (a+b)^3=a^3+3a^2b+3ab^2+b^3
- (a-b)^3=a^3-3a^2b+3ab^2-b^3
- (a+b)^3+(a-b)^3 = 2a^3+6ab^2
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