Question

(a + 2b)² - (2a + b)²​

Answer 1

Expand the square
(

+
2

)
2
−
1
(
2

+

)
2
(
a
+
2
b
)
2
−
1
(
2
a
+
b
)
2
(a+2b)2−1(2a+b)2
(

+
2

)
(

+
2

)
−
1
(
2

+

)
2
(
a
+
2
b
)
(
a
+
2
b
)
−
1
(
2
a
+
b
)
2
(a+2b)(a+2b)−1(2a+b)2
2
Distribute
(

+
2

)
(

+
2

)
−
1
(
2

+

)
2
(
a
+
2
b
)
(
a
+
2
b
)
−
1
(
2
a
+
b
)
2
(a+2b)(a+2b)−1(2a+b)2

(

+
2

)
+
2

(

+
2

)
−
1
(
2

+

)
2
a
(
a
+
2
b
)
+
2
b
(
a
+
2
b
)
−
1
(
2
a
+
b
)
2
a(a+2b)+2b(a+2b)−1(2a+b)2
3
Distribute

(

+
2

)
+
2

(

+
2

)
−
1
(
2

+

)
2
a
(
a
+
2
b
)
+
2
b
(
a
+
2
b
)
−
1
(
2
a
+
b
)
2
a(a+2b)+2b(a+2b)−1(2a+b)2

2
+
2


+
2

(

+
2

)
−
1
(
2

+

)
2
a
2
+
2
a
b
+
2
b
(
a
+
2
b
)
−
1
(
2
a
+
b
)
2
a2+2ab+2b(a+2b)−1(2a+b)2
4
Distribute

2
+
2


+
2

(

+
2

)
−
1
(
2

+

)
2
a
2
+
2
a
b
+
2
b
(
a
+
2
b
)
−
1
(
2
a
+
b
)
2
a2+2ab+2b(a+2b)−1(2a+b)2

2
+
2


+
2


+
4

2
−
1
(
2

+

)
2
a
2
+
2
a
b
+
2
a
b
+
4
b
2
−
1
(
2
a
+
b
)
2
a2+2ab+2ab+4b2−1(2a+b)2
5
Combine like terms

2
+
2


+
2


+
4

2
−
1
(
2

+

)
2
a
2
+
2
a
b
+
2
a
b
+
4
b
2
−
1
(
2
a
+
b
)
2
a2+2ab+2ab+4b2−1(2a+b)2

2
+
4


+
4

2
−
1
(
2

+

)
2
a
2
+
4
a
b
+
4
b
2
−
1
(
2
a
+
b
)
2
a2+4ab+4b2−1(2a+b)2