Junghune N. answered • 03/05/18
Tutor
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Providing Strategies to Solve Problems in Math and Science
If I am understanding your question correctly, then I would solve this problem like this:
Since we want to add a single term (monomial) to the given binomial (36-12x) such that the resulting trinomial can be rewritten as the square of another binomial, then we want to make sure our resulting trinomials are of the following form:
a2-2ab+b2 or a2+2ab+b2
since:
a2-2ab+b2 = (a-b)2
and
a2+2ab+b2 = (a+b)2
In the above equations, we have a trinomial being expressed as a square of a binomial.
Knowing that the above equations are true, we can work with our given binomial and solve backwards from there:
36–12x -> a = x, b = 6
Because a = x, the monomial that we want to add to 36–12x is x2.
The resulting trinomial is: x2 -12x + 36 = (x-6)2
And thus, we have a trinomial expressed as the square of a binomial.
Since we want to add a single term (monomial) to the given binomial (36-12x) such that the resulting trinomial can be rewritten as the square of another binomial, then we want to make sure our resulting trinomials are of the following form:
a2-2ab+b2 or a2+2ab+b2
since:
a2-2ab+b2 = (a-b)2
and
a2+2ab+b2 = (a+b)2
In the above equations, we have a trinomial being expressed as a square of a binomial.
Knowing that the above equations are true, we can work with our given binomial and solve backwards from there:
36–12x -> a = x, b = 6
Because a = x, the monomial that we want to add to 36–12x is x2.
The resulting trinomial is: x2 -12x + 36 = (x-6)2
And thus, we have a trinomial expressed as the square of a binomial.
