MATH SOLVE

2 months ago

Q:
# 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

Accepted Solution

A:

a perfect square trinomial can be factored into the form

[tex](a+b)^2[/tex]

the expansion is

[tex]a^2+2ab+b^2[/tex]

so if we say that a=m then

[tex](m+b)^2=m^2+2mb+b^2[/tex]

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.

[tex]m^2+10m+100[/tex]

10m is the 2mb term

10 is the coefient, 10/2=5, 5^2=25, 25β 100, so not a perfect square trinomial

B.

[tex]m^2+10m+25[/tex]

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

C.

[tex]m^2+24m+144[/tex]

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

D.

[tex]m^2+36m+60[/tex]

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

answers are B and C

[tex](a+b)^2[/tex]

the expansion is

[tex]a^2+2ab+b^2[/tex]

so if we say that a=m then

[tex](m+b)^2=m^2+2mb+b^2[/tex]

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.

[tex]m^2+10m+100[/tex]

10m is the 2mb term

10 is the coefient, 10/2=5, 5^2=25, 25β 100, so not a perfect square trinomial

B.

[tex]m^2+10m+25[/tex]

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

C.

[tex]m^2+24m+144[/tex]

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

D.

[tex]m^2+36m+60[/tex]

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

answers are B and C