Fill in the blank to make the trinomial a perfect square trinomial. $64 s ^ { 4 } + \underline { ( \quad ) }+ 81$
A) $64 s ^ { 4 } + \underline { \left( 72 s ^ { 2 } \right) } + 81$
B) $64 s ^ { 4 } + \underline { \left( 144 s ^ { 2 } \right) } + 81$
C) $64 s ^ { 4 } + ( \underline { 144 s } ) + 81$
D) $64 s ^ { 4 } + { \left( 36 s ^ { 2 } \right) } + 81$

Question

Fill in the blank to make the trinomial a perfect square trinomial. $64 s ^ { 4 } + \underline { ( \quad   ) }+ 81$
A) $64 s ^ { 4 } + \underline { \left( 72 s ^ { 2 } \right) } + 81$
B) $64 s ^ { 4 } + \underline { \left( 144 s ^ { 2 } \right) } + 81$
C) $64 s ^ { 4 } + ( \underline { 144 s } ) + 81$
D) $64 s ^ { 4 } +  { \left( 36 s ^ { 2 } \right) } + 81$

Quizplus · Accepted Answer

A trinomial is a perfect square trinomial if it can be written in the form $(ax)^2 + 2abx + b^2$. Here, $a^2 = 64s^4$ (so $a = 8s^2$) and $b^2 = 81$ (so $b = 9$). The middle term should be $2ab = 2(8s^2)(9) = 144s^2$.

Fill in the Blank to Make the Trinomial a Perfect 64s4+()‾+8164 s ^ { 4 } + \underline { ( \quad ) }+ 8164s4+()​+81

Fill in the Blank to Make the Trinomial a Perfect $64 s ^ { 4 } + \underline { ( \quad ) }+ 81$