Question

what should be the middle term to make this perfect square trinomial m² + _ +100?​

Answer 1

Answer:

Divide the coefficient for

y

by

2

, then square the result. This will give you the missing term.

1

2

2

=

1

2

⋅

1

2

=

1

4

.

(

1

4

)

2

=

1

16

Solution:

y

2

+

1

2

y

+

1

16

Answer 2

To find:

The middle term that makes $m^{2}+_+100$ a perfect square

Step-by-step explanation:

Now $m^{2}+_{} +100$

$=(m)^{2}+2\times m\times 10+(10)^{2}$

$=(m+10)^{2}$

• Using the algebraic identity $(a+b)^{2}=a^{2}+2ab+b^{2}$

Here, $(m+10)^{2}$ certainly is a perfect square, which has become possible when we have taken $2\times m\times 10=20m$ in the blank space.

Answer:

Thus $20m$ should be the middle term to make the given term a perfect trinomial.

Note:

We can also take the middle term to be $(-20m)$ which gives the perfect square $(m-10)^{2}$.