Factor 25x^2+40x+16

Problem

25*x^2+40*x+16

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

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

4. Verify the middle term: $2(5x)(4) = 40x$, which matches the given expression.

5. Apply the perfect square trinomial formula to factor the expression.

Final Answer

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

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