Squaring a Binomial

​
visualization
1
2
a
8
a+b
20
show equation
The square of a sum is the sum of the squares plus twice the cross term. Here is the general case, some special cases, and squaring a trinomial:
2
(a+b)
=
2
a
+2ab+
2
b
2
(a+1)
=
2
a
+2a+1
(
2
a+2)
=
2
a
+4a+4
2
(a-b)
=
2
a
-2ab+
2
b
2
(
2
a
+
2
b
)
=
4
a
+2
2
a
2
b
+
4
b
2
(a+b+c)
=​​
2
a
+2a(b+c)+
2
(b+c)
=​​
2
a
+2ab+2ac+
2
b
+2bc+
2
c
=​​
2
a
+
2
b
+
2
c
+2(ab+bc+ca)

External Links

Binomial (Wolfram MathWorld)

Permanent Citation

Jesse Nochella
​
​"Squaring a Binomial"​
​http://demonstrations.wolfram.com/SquaringABinomial/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011