Factor 16x^2+40x+25

Problem

16*x^2+40*x+25

Solution

1. Identify the structure of the quadratic expression, noting that the first and last terms are perfect squares.

2. Rewrite the first term as (4*x)^2 and the last term as 5^2

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

2*(4*x)*(5)=40*x

4. Apply the formula for a perfect square trinomial a^2+2*a*b+b^2=(a+b)^2 where a=4*x and b=5

Final Answer

16*x^2+40*x+25=(4*x+5)^2

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