Question

Fill in the blank with a number to make the expression a perfect square. w? + 10w +

Answer 1

$\boxed{w^2+10w+25}$

Explanation:

A Perfect-Square Trinomials are quadratics that result after squaring binomials. So these Perfect-square trinomials are given in the form:

$a^2x^2\pm 2axb+b^2$

Whose Squared-Binomial Form is:

$(ax \pm b)^2$

In this exercise, we have the variable $w$, so changing $x \ by \ w$ it is true that:

$a^2w^2\pm 2awb+b^2=(aw \pm b)^2$

Therefore, for our given expression we have:

$w?+10w+$

So our goal is to complete this expression:

Step 1. First of all, we need to square our variable w. therefore:

$w^2+10w+$

Step 2. Here $a=1$

Step 3. Let's find b:

$2wb=10w \\ \\ 2bw=10w \\ \\ So: \\ \\ 2b=10 \\ \\ Where: \\ \\ b=\frac{10}{2} \\ \\ \boxed{b=5}$

Finally, our complete expression is:

$\boxed{w^2+10w+25}$

Learn more:

Factors of polynomials: brainly.com/question/1554148

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