Factor 25x^2-10x+1

Problem

25*x2−10*x+1

Solution

1. Identify the expression as a quadratic trinomial of the form a*x2+b*x+c where a=25 b=−10 and c=1

2. Recognize that the first term 25*x2 is a perfect square (5*x)2 and the last term 1 is a perfect square (1)2

3. Check if the middle term fits the pattern for a perfect square trinomial a2−2*a*b+b2=(a−b)2

4. Verify the middle term by calculating 2(5x)(1) = 10x,w*h*i*c*h*m*a*t*c*h*e*s(t)*h*e*g*i*v*e*n*m*i*d(d(l))*e*t*e*r*m10x$ when using the subtraction sign.

5. Apply the formula for a perfect square trinomial to write the factored form.

Final Answer

25*x2−10*x+1=(5*x−1)2

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