Factor 25x^2-10x+1

Problem

25*x^2−10*x+1

Solution

1. Identify the expression as a quadratic trinomial of the form a*x^2+b*x+c where a=25 b=−10 and c=1

2. Recognize that the first term 25*x^2 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 a^2−2*a*b+b^2=(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*x^2−10*x+1=(5*x−1)^2

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