Math, asked by abhi6130, 1 year ago

a³+b³ and a³-b³ formulas

Answers

Answered by mysticd
194

Answer:

i) + = (a+b)(-ab+)

Or

= (a+b)³-3ab(a+b)

ii) -b³ = (a-b)(+ab+)

Or

= (a-b)³+3ab(a-b)

Explanation:

i) We know the algebraic identity:

+3a²b+3ab²+ = (a+b)³

=> ++3ab(a+b)=(a+b)³

=> += (a+b)³-3ab(a+b)---(1)

= (a+b)[(a+b)²-3ab]

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

= (a+b)(-ab+) ----(2)

Now ,

ii) By algebraic identity:

-3a²b+3ab²-b³ = (a-b)³

b)³=> a³--3ab(a-b)=(a-b)³

b)³=> a³-b³ = (a-b)³+3ab(a-b)---(3)

)= (a-b)[(a-b)²+3ab]

3ab]= (a-b)(a²-2ab+b²+3ab)

3ab)= (a-b)(a²+ab+b²) ----(4)

Therefore,

i)+ = (a+b)(-ab+)

Or

= (a+b)³-3ab(a+b)

ii) -b³ =(a-b)(+ab+)

Or

= (a-b)³+3ab(a-b)

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