Question

Which trinomials are perfect square trinomials? Select each correct answer.

A) m^2+10m+100
B) m^2+10m+25
C) m^2+24m+144
D) m^2+36m+60

Answer 1

a perfect square trinomial can be factored into the form

`(a+b)^2`
the expansion is

`a^2+2ab+b^2`
so if we say that a=m then

`(m+b)^2=m^2+2mb+b^2`
basically, if you take the coefient (number part) of the 2mb term and divide it by 2 and square it, you should get the last term

(coefient is the number part, like in 4m, 4 is the coefient)

A.

`m^2+10m+100`
10m is the 2mb term
10 is the coefient, 10/2=5, 5^2=25, 25≠100, so not a perfect square trinomial

B.

`m^2+10m+25`
as from before, 10 is coefient, 10/2=5, 5^2=25, 25=25, yep, this is perfect square trinomial

C.

`m^2+24m+144`
24m is the 2mb term, 24 is coefient, 24/2=12, 12^2=144, 144=144, yep this is a perfect square trinomail

D.

`m^2+36m+60`
36m is the 2mb term, 36 is the coefient, 36/2=18, 18^2=324, 324≠60, so not a perfect square trinomial



answers are B and C