Question

practice completing perfect square trinomials.
what constant term is necessary to complete the perfect square trinomial pictured in the algebra tiles?
x² + 8x + \boxed{}

Explanation:

Step1: Recall the formula for perfect square trinomial

A perfect square trinomial is of the form \(x^2 + 2bx + b^2=(x + b)^2\). In the given expression \(x^2+8x+\square\), we can see that \(2b = 8\).

Step2: Solve for \(b\)

From \(2b=8\), divide both sides by 2: \(b=\frac{8}{2}=4\).

Step3: Find the constant term

The constant term of the perfect square trinomial is \(b^2\). Substitute \(b = 4\) into \(b^2\), we get \(b^2=4^2 = 16\).

Answer:

16