Question

Find an expression equivalent to x^2 + 8x + 3 that includes a perfect square binomial.

Answer 1

(x +4)^2 -13

Explanation:

A binomial cannot be a perfect square, so we interpret the problem to mean "find an equivalent expression than includes the square of a binomial."

The equivalent expression we're usually interested in is the one known as "vertex form." We can add and subtract the square of half the x-coefficient to help find that form:

(x^2 +8x +16) +(3 -16) . . . . . . . we added (8/2)^2 -(8/2)^2

(x +4)^2 -13 . . . . . . . . . . . . . . . express the trinomial as a square, simplify