Factor 4x^2+25

Problem

4*x2+25

Solution

1. Identify the expression as a sum of two squares, which follows the form a2+b2

2. Determine the values of a and b by taking the square roots of each term: a=√(,4*x2)=2*x and b=√(,25)=5

3. Apply the formula for factoring a sum of squares over the complex numbers, which is a2+b2=(a+b*i)*(a−b*i)

4. Substitute the values into the formula to obtain the factors.

Final Answer

4*x2+25=(2*x+5*i)*(2*x−5*i)

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