Question

Which polynomial is a perfect square trinomial?

36x2 − 18x − 9

4a2 − 28a − 49

25b2 − 40b + 16

4x2 − 6x + 9

Answer 1

a perfect square is

\[(a + b)^2 = a^2 + 2ab + b^2\]

a perfect square has the 1st and last terms positive... as squaring any negative gives a positive.

and notice the middle term is double the product of a and b.

hope this helps...

Answer 2

eh

Answer 3

since the middle term in each is negative then

\[(a -b)^2 = a^2 - 2ab + b^2\]

is the expansion...

Answer 4

ok... for the 1st choice

are the 1st and last terms positive..?

Answer 5

no..

Answer 6

ok... so the same logic can be applied to the 2nd choice...

on now the 3rd choice

using the expansion above

you are beaing with 5b and -4...

is the middle term.. double the product of 5b and - 4


for the last choice you are looking at

2x and -3... is the middle term double the product of 2x and - 3..?

Answer 7

so 25b2 − 40b + 16?

Answer 8

thats the correct solution... well done...

I forgot to say

\[25b^2 = (5b)^2 ...and....16 = (-4)^2\]

the reason I know its -4 is that the middle term is negative.