Question

enter the correct value so that each expression is a perfect - square trinomial.
x² - 10x + \square
done

Explanation:

Step1: Recall perfect - square trinomial formula

A perfect - square trinomial has the form \(a^{2}-2ab + b^{2}=(a - b)^{2}\). For the given expression \(x^{2}-10x+\square\), we can compare it with \(a^{2}-2ab + b^{2}\). Here, \(a = x\) and \(-2ab=-10x\).

Step2: Solve for \(b\)

Substitute \(a = x\) into \(-2ab=-10x\). We get \(-2\times x\times b=-10x\). Divide both sides of the equation by \(-2x\) (assuming \(x
eq0\)). \(\frac{-2xb}{-2x}=\frac{-10x}{-2x}\), which simplifies to \(b = 5\).

Step3: Find the value of \(b^{2}\)

Since the third term of the perfect - square trinomial is \(b^{2}\), and we found that \(b = 5\), then \(b^{2}=5^{2}=25\). So the expression \(x^{2}-10x + 25=(x - 5)^{2}\), which is a perfect - square trinomial.

Answer:

25