because 90 is not a perfect square
(a-b)^2 = a^2 - 2ab + b^2
Writing: How can you tell that
x^2−19x+90
is not a perfect square trinomial?
2 answers
Perfect square trinomials be expressed in squared binomial form as:
( a x ± b )² = ( a x ± b ) ( a x ± b )
In this case:
x² - 19 x + 90 = ( x - 9 ) ( x - 10 )
It's not a perfect square because the members in parentheses are different.
For example:
x² - 18 x + 81 = ( x - 9 ) ( x - 9 ) = ( x - 9 )²
is a perfect square
and
x² - 20 x + 100 = ( x - 10 ) ( x - 10 ) = ( x - 10 )²
is a also perfect square
( a x ± b )² = ( a x ± b ) ( a x ± b )
In this case:
x² - 19 x + 90 = ( x - 9 ) ( x - 10 )
It's not a perfect square because the members in parentheses are different.
For example:
x² - 18 x + 81 = ( x - 9 ) ( x - 9 ) = ( x - 9 )²
is a perfect square
and
x² - 20 x + 100 = ( x - 10 ) ( x - 10 ) = ( x - 10 )²
is a also perfect square