Factor 16x^2+25

Problem

16*x2+25

Solution

1. Identify the form of the expression. The expression 16*x2+25 is a sum of two squares because 16*x2=(4*x)2 and 25=5

2. Apply the formula for the sum of squares. Over the set of real numbers, a sum of squares is irreducible. However, over the set of complex numbers, it follows the pattern a2+b2=(a+b*i)*(a−b*i)

3. Substitute the values a=4*x and b=5 into the complex factoring formula.

4. Write the final factored form using the imaginary unit i

Final Answer

16*x2+25=(4*x+5*i)*(4*x−5*i)

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