[tex]\boxed{w^2+10w+25}[/tex]
A Perfect-Square Trinomials are quadratics that result after squaring binomials. So these Perfect-square trinomials are given in the form:
[tex]a^2x^2\pm 2axb+b^2[/tex]
Whose Squared-Binomial Form is:
[tex](ax \pm b)^2[/tex]
In this exercise, we have the variable [tex]w[/tex], so changing [tex]x \ by \ w[/tex] it is true that:
[tex]a^2w^2\pm 2awb+b^2=(aw \pm b)^2[/tex]
Therefore, for our given expression we have:
[tex]w?+10w+[/tex]
So our goal is to complete this expression:
Step 1. First of all, we need to square our variable w. therefore:
[tex]w^2+10w+[/tex]
Step 2. Here [tex]a=1[/tex]
Step 3. Let's find b:
[tex]2wb=10w \\ \\ 2bw=10w \\ \\ So: \\ \\ 2b=10 \\ \\ Where: \\ \\ b=\frac{10}{2} \\ \\ \boxed{b=5}[/tex]
Finally, our complete expression is:
[tex]\boxed{w^2+10w+25}[/tex]
Factors of polynomials: https://brainly.com/question/1554148
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