Use a special product pattern to find the product $9 u + ( v + 10 ) ] ^ { 2 }$ .

A) $81 u ^ { 2 } + v ^ { 2 } + 18 u v + 180 u + 20 v + 100$
B) $81 u ^ { 2 } + v ^ { 2 } + 20 v + 100$
C) $81 u ^ { 2 } + v ^ { 2 } + 180 u + 20 v + 100$
D) $81 u ^ { 2 } + v ^ { 2 } + 100$
E) $81 u ^ { 2 } + v ^ { 2 } + 18 u v + 20 v + 100$

Question

Use a special product pattern to find the product

9 u + ( v + 10 ) ] ^ { 2 }

.

A)

81 u ^ { 2 } + v ^ { 2 } + 18 u v + 180 u + 20 v + 100

B)

81 u ^ { 2 } + v ^ { 2 } + 20 v + 100

C)

81 u ^ { 2 } + v ^ { 2 } + 180 u + 20 v + 100

D)

81 u ^ { 2 } + v ^ { 2 } + 100

E)

81 u ^ { 2 } + v ^ { 2 } + 18 u v + 20 v + 100

Nguy?n Ph?ng · Accepted Answer

Final Answer : A, Explanation :   The correct expansion using the special product pattern  (a+b)^2 = a^2 + 2ab + b^2  for  a = 9u  and  b = v + 10  gives  81u^2 + 2(9u)(v+10) + (v+10)^2 , which simplifies to  81u^2 + 18uv + 180u + v^2 + 20v + 100 .

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