What term should be added to y 2 − 1 5 y y ^ { 2 } - \frac { 1 } { 5 } y y 2 − 5 1 y to make it a perfect square trinomial?A) 5B) 1 100 \frac { 1 } { 100 } 100 1 C) 100D) 5 2 \frac{5}{2} 2 5 E) 1 50 \frac { 1 } { 50 } 50 1

Question

What term should be added to   y 2 − 1 5 y y ^ { 2 } - \frac { 1 } { 5 } y y 2 − 5 1 ​ y   to make it a perfect square trinomial?A)  5B)    1 100 \frac { 1 } { 100 } 100 1 ​ C)  100D)    5 2  \frac{5}{2}  2 5 ​ E)    1 50 \frac { 1 } { 50 } 50 1 ​

maria sarah salen · Accepted Answer

Final Answer : B, Explanation :   To make   y 2 − 1 5 y y^2 - \frac{1}{5}y y 2 − 5 1 ​ y   a perfect square trinomial, you need to add the square of half the coefficient of   y y y  . Half of   − 1 5 -\frac{1}{5} − 5 1 ​   is   − 1 10 -\frac{1}{10} − 10 1 ​  , and squaring this gives   ( − 1 10 ) 2 = 1 100 \left(-\frac{1}{10}\right)^2 = \frac{1}{100} ( − 10 1 ​ ) 2 = 100 1 ​  .

What term should be added to $\frac { 1 } { 5 } y$ to make it a perfect square trinomial?

A) 5
B) $1100\frac { 1 } { 100 }$
C) 100
D) $\frac{5}{2}$
E) $150\frac { 1 } { 50 }$

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What term should be added to y2−15yy ^ { 2 } - \frac { 1 } { 5 } yy2−51​y to make it a perfect square trinomial?A) 5B) 1100\frac { 1 } { 100 }1001​ C) 100D) 52 \frac{5}{2} 25​ E) 150\frac { 1 } { 50 }501​

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Learning Objectives

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What term should be added to $\frac { 1 } { 5 } y$ to make it a perfect square trinomial?

A) 5
B) $1100\frac { 1 } { 100 }$
C) 100
D) $\frac{5}{2}$
E) $150\frac { 1 } { 50 }$