Given: (a+b)3 ( a + b ) 3

prove: (a+b)3=a3+3a2b+3ab2+b3

(
a
+
b
)
3
=
a
3
+
3
a
2
b
+
3
a
b
2
+
b
3

statements reasons
1 (a+b)3
(
a
+
b
)
3
given
2 (a+b)(a+b)(a+b)
(
a
+
b
)
(
a
+
b
)
(
a
+
b
)
rewrite the power as a product of the base.
3 (a+b)(a2+ab+ab+b2)
(
a
+
b
)
(
a
2
+
a
b
+
a
b
+
b
2
)
distributive property
4 (a+b)(a2+2ab+b2)
(
a
+
b
)
(
a
2
+
2
a
b
+
b
2
)
combine like terms.
5 _[blank]_ distributive property
6 a3+3a2b+3ab2+b3
a
3
+
3
a
2
b
+
3
a
b
2
+
b
3
combine like terms.