Question

verification of the identity (a + b)3 =a3+3ab (a + b) + b3

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

(a+b)³=a³+3ab+3ab²+b³

Step-by-step explanation:

LHS=(a+b)^{3}LHS=(a+b)

3

=(a+b)(a+b)^{2}(a+b)(a+b)

2

=(a+b)(a^{2}+2ab+b^{2})(a+b)(a

2

+2ab+b

2

)

/* By algebraic identity:

\boxed {(x+y)^{2}=x^{2}+2xy+y^{2}}

(x+y)

2

=x

2

+2xy+y

2

*/

=a(a^{2}+2ab+b^{2})+b(a^{2}+2ab+b^{2})a(a

2

+2ab+b

2

)+b(a

2

+2ab+b

2

)

= a^{3}+2a^{2}b+ab^{2}+a^{2}b+2ab^{2}+b^{3}a

3

+2a

2

b+ab

2

+a

2

b+2ab

2

+b

3

=a^{3}+(2+1)a^{2}b+(1+2)ab^{2}+b^{3}a

3

+(2+1)a

2

b+(1+2)ab

2

+b

3

= a^{3}+3a^{2}b+3ab^{2}+b^{3}a

3

+3a

2

b+3ab

2

+b

3

=RHSRHS

Therefore