m(squared)-8m+n
Find the value on n such that each expression is a perfect square trinomial.
To find the value of 'n' such that the given expression is a perfect square trinomial, we need to set the expression equal to a perfect square trinomial and then compare the coefficients.
A perfect square trinomial can be expressed in the form of (a + b)^2, where 'a' and 'b' are constants.
Let's rewrite the expression with variables 'm' and 'n' in the form of a perfect square trinomial:
m^2 - 8m + n = (a + b)^2
Expanding (a + b)^2 using the binomial formula, we get:
m^2 - 8m + n = a^2 + 2ab + b^2
Comparing the coefficients of the like terms on both sides, we get:
a^2 = m^2
2ab = -8m
b^2 = n
From the second equation, we can solve for 'b' in terms of 'm':
2ab = -8m
b = (-8m) / (2a)
b = -4m / a
Substituting the value of 'b' into the third equation, we have:
(-4m / a)^2 = n
16m^2 / a^2 = n
So, for the expression to be a perfect square trinomial, the value of 'n' is equal to 16m^2 / a^2.