Learn all Concepts of Polynomials Class 9 (with VIDEOS). Check - Polynomials Class 9

Identity V is

(a + b + c)
^{
2
}
= a
^{
2
}
+ b
^{
2
}
+ c
^{
2
}
+ 2ab + 2bc + 2ca

Let us prove it

Proof :

(a + b + c)
^{
2
}

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

*
Using (x + y)
^{
2
}
= x
^{
2
}
+ y
^{
2
}
+ 2xy
*

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

= (a + b)
^{
2
}
+ c
^{
2
}
+ 2ac + 2bc

*
Using (x + y)
^{
2
}
= x
^{
2
}
+ y
^{
2
}
+ 2xy
*

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

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

Check more algebra formulas .

Lets take an example

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

(2 + 3 + 4)2 = 22 + 32 + 42 + 2(2)(3) + 2(3)(4) + 2(4)(2)

(9)2 = 4 + 9 + 16 + 12 + 24 + 16

81 = 4 + 9 + 16 + 12 + 24 + 16

81 = 81