Factor 9x^2-30x+25

Problem

9*x^2−30*x+25

Solution

1. Identify the structure of the quadratic expression a*x^2+b*x+c where a=9 b=−30 and c=25

2. Recognize that the first term 9*x^2 is a perfect square, (3*x)^2 and the last term 25 is a perfect square, 5^2

3. Check if the middle term matches the pattern for a perfect square trinomial (A−B)^2=A^2−2*A*B+B^2

4. Verify the middle term by calculating 2*A*B $2(3x)(5) = 30x.S*i*n*c*e*t*h*e*m*i*d(d(l))*e*t*e*r*m*i*s()30x,t*h*e*e*x*p*r*e*s(s(i))*o*n*ƒ*i*t*s(t)*h*e*p*a*t*t*e*r*n3x - 5)^2$.

5. Write the factored form as the square of the binomial.

Final Answer

9*x^2−30*x+25=(3*x−5)^2

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