Replace ∗ with a monomial so that the trinomial may be represented by a square of a binomial: 36–12x + ∗, and 25a^2+ ∗ + .25 b^2
5ab
I need help with the first one...
To represent the trinomial 36 - 12x + ∗ as a square of a binomial, we need to find a monomial that, when squared, results in the trinomial. Here's how we can do that step by step:
Step 1: Identify the first term of the trinomial.
In the case of 36 - 12x + ∗, the first term is 36.
Step 2: Take the square root of the first term.
The square root of 36 is 6.
Step 3: Identify the second term of the trinomial.
In the case of 36 - 12x + ∗, the second term is -12x.
Step 4: Take half of the coefficient of the second term and square it.
Half of -12 is -6, and squaring it gives us 36.
Step 5: Replace ∗ with the square we obtained.
In this case, the monomial that can be used as a replacement for ∗ to represent the given trinomial as a square of a binomial is 36.
Therefore, the trinomial 36 - 12x + 36 can be represented as the square of the binomial (6 - 2x).
I need help with just the second one
25a^2+ ∗ + .25 b^2
You know it must look something like:
(5a ± .5b)^2 , expand to see the middle term
take your pick