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

  (x +4)^2 -13

Step-by-step 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

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step-by-step explanation: