Identify Structure: Identify the structure of the expression d^2 - 20d + 100. This is a quadratic expression in the form of d^2 - (2*10)d + 10^2.Recognize Perfect Square Trinomial: Recognize that the quadratic expression is a perfect square trinomial. A perfect square trinomial takes the form (a - b)^2 = a^2 - 2ab + b^2. In our case, a = d and b = 10, so the expression d^2 - 20d + 100 fits the pattern of (d - 10)^2.Write as Squared Binomial: Write the expression as a squared binomial. Since the expression matches the pattern of a perfect square trinomial, we can write it as (d - 10)^2.Check by Expanding: Check the result by expanding (d - 10)^2 to ensure it matches the original expression. Expanding (d - 10)^2 gives d^2 - 2*10*d + 10^2, which simplifies to d^2 - 20d + 100. This matches the original expression, confirming that the simplification is correct.

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$d^{2}-20 d+100$

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Algebra 2

Evaluate rational exponents

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d^{2}-20 d+100

Identify Structure: Identify the structure of the expression $d^2 - 20d + 100$ . This is a quadratic expression in the form of $d^2 - (2\times 10)d + 10^2$ .
Recognize Perfect Square Trinomial: Recognize that the quadratic expression is a perfect square trinomial. A perfect square trinomial takes the form $(a - b)^2 = a^2 - 2ab + b^2$ . In our case, $a = d$ and $b = 10$ , so the expression $d^2 - 20d + 100$ fits the pattern of $(d - 10)^2$ .
Write as Squared Binomial: Write the expression as a squared binomial. $\newline$ Since the expression matches the pattern of a perfect square trinomial, we can write it as $(d - 10)^2$ .
Check by Expanding: Check the result by expanding $(d - 10)^2$ to ensure it matches the original expression. $\newline$ Expanding $(d - 10)^2$ gives $d^2 - 2\times 10\times d + 10^2$ , which simplifies to $d^2 - 20d + 100$ . $\newline$ This matches the original expression, confirming that the simplification is correct.