Factor 25x^2-40x+16

Problem

25*x2−40*x+16

Solution

1. Identify the structure of the trinomial as a potential perfect square trinomial of the form a2−2*a*b+b2

2. Determine the square root of the first term 25*x2 which is 5*x

3. Determine the square root of the last term 16 which is 4

4. Verify the middle term by calculating 2*a*b which is 2(5x)(4) = 40x.S*i*n*c*e*t*h*e*m*i*d(d(l))*e*t*e*r*m*i*n*t*h*e*e*x*p*r*e*s(s(i))*o*n*i*s()40x,t*h*e*e*x*p*r*e*s(s(i))*o*n*ƒ*i*t*s(t)*h*e*p*a*t*t*e*r*na - b)^2$.

5. Write the factored form using the values a=5*x and b=4

Final Answer

25*x2−40*x+16=(5*x−4)2

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