Question #bd0e0
↳Redirected from
"How do covalent bonds affect physical properties?"
You can't. This expression is unfactorable.
A perfect square trinomial is a trinomial (a polynomial with three terms) that can be factored down into one of two forms:
1) #(a+b)^2#
or
2) #(a-b)^2#
If we expand both of those out, we get
1) #(a+b)^2=a^2+2ab+b^2#
and
2) #(a-b)^2=a^2-2ab+b^2#
Let's see if #x^2-7x+49# is a perfect square trinomial. According to the expansion, we see that the first and last term have to be perfect squares. Let's check that:
#x^2# and #49# are the first and last term, respectively.
#sqrt(x^2)=x# and #sqrt(49)=+-7#
The two terms are perfect squares! Now let's see - the middle term has to be twice the product of the two squares.
Our two squares are #x# and #+-7# (NOTE: We have two different combinations for #+-7#: #+7# and #-7#, so we have to test both of them to see if they fit the properties of the middle term of a perfect square term).
#(2)(x)(+7)=14x#
Nope. Let's try the other combination:
#(2)(x)(-7)=-14x#
Nope either. Even though our first and last terms were perfect squares, the middle term did not have the properties of a perfect square trinomial.
Therefore, #x^2-7x+49# is not a perfect square trinomial. And so, it cannot be expressed as the product of two binomials.
