Question

to verify the identity(a+b)^3=a^3+3ab^2+3ab^2+b^3

Answer 1

(a+b)³ = a³+3a²b+3ab²+b³

Let's solve LHS. →

(a+b)³

→ (a+b)(a+b)(a+b)

→ a(a+b)(a+b)+b(a+b)(a+b)

→ (a²+ab)(a+b)+(ab+b²)(a+b)

→ a(a²+ab)+b(a²+ab)+a(ab+b²)+b(ab+b²)

→ a³+a²b+a²b+ab²+a²b+ab²+ab²+b³

→ a³+3a²b+3ab²+b³

Hence , LHS = RHS
Verified
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Answer 2

Hi friend,

Need to prove:-

(a+b)³ = a³+3a²b+3ab²+b³

==========================

Take LHS:-

(a+b)³

= (a+b)(a+b)(a+b)

= (a+b)²(a+b)

= {a²+b²+2ab} (a+b)

= a²(a+b) + b²(a+b) + 2ab(a+b)

= a³+a²b+ab²+b³+2a²b+2ab²

= a³+b³+3a²b+3ab²

= a³+3a²b+3ab²+b³

LHS = RHS

Hence verified!

Hope it helps