Question

verify the algebraic identity: (a+b+c)²=a²+b²+c²+2ab+2bc +2ca



pls give the accurate answer!!!​

Answer 1

Answer:

Step-by-step explanation:

(a+b+c)^2

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

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

                                                                         (distributive law)

=a*a+a*b+a*c+b*a+b*b+b*c+c*a+c*b+c*c

                                                                         (distributive law)

=a^2+ab+ac+ba+b^2+bc+ca+cb+c^2

=a^2+b^2+c^2+ab+ba+bc+cb+ca+ac

                                                                        (by rearranging)

=a^2+b^2+c^2+ab+ab+bc+bc+ac+ac

                                                                        (commutative law)

=a^2+b^2+c^2+2ab+2bc+2ca

HENCE VERIFIED

Answer 2

Step-by-step explanation:

solution:

L.H.S:

=(a+b)³

=(a+b)(a²+2ab+b²)

=a(a²+2ab+b²)+b(a²+2ab+b²)

=a³+2a²b+ab²+ba²+2ab²+b³

=a³+2a²b+ba²+2ab²+ab²+b³

=a³+b³+3a²b+3ab²

R.H.S:

=a³+b³+3a²b+3ab²

Therefore L.H.S = R.H.S verified