Question

insert a monomial so that the expression becomes the square of a binomial.\\(x^2 + 4x + ....\\)\
answer\\(x^2 + 4x + \square\\)

Explanation:

Step1: Recall the square of a binomial formula

The square of a binomial \((a + b)^2=a^2 + 2ab + b^2\). In the given expression \(x^{2}+4x+\dots\), we have \(a = x\) and \(2ab=4x\).

Step2: Solve for \(b\)

Substitute \(a = x\) into \(2ab = 4x\), we get \(2\times x\times b=4x\). Divide both sides by \(2x\) (assuming \(x
eq0\)), we have \(b=\frac{4x}{2x} = 2\).

Step3: Find the constant term \(b^{2}\)

Since \(b = 2\), then \(b^{2}=2^{2}=4\). So the monomial to insert is \(4\) so that \(x^{2}+4x + 4=(x + 2)^{2}\).

Answer:

\(4\)