Question

which polynomials are perfect square trinomials: 9x^2 − 6x + 1...........36b^2 − 24b + 8..........16x^2 + 24x+ 9...........4a^2 − 10a + 25

Answer 1

well a perfect trinomial... has 3 terms...

(ax + b)^2 = a^2x^2 + 2abx + b^2

or

(ax - b)^2 = a^2b^2 -2abx + b^2

so look for 1st and last terms that are squares

and a middle term that is double the product of the 1st and last.

so looking at the 1st expression

9x^2 = (3x)^2

1 = (1)^2

so double the product will be -6x or 6x

which you seem to have so the 1st expression can be written as

(3x - 1)^2 = 9x^2 - 6x + 1

hope it makes sense and helps

Answer 2

thanks

Answer 3

the 2nd equation isn't a perfect square as 8 isn't a square number