Factor the perfect square trinomial 25n² + 40np + 16p²:
To factor a perfect square trinomial, follow these steps:
1. Identify if the trinomial fits the pattern (a² + 2ab + b²) where a is the square root of the first term, b is the square root of the last term, and the middle term is 2ab.
2. In this case, the first term is 25n², the last term is 16p². The square root of 25n² is 5n, and the square root of 16p² is 4p.
3. Check if the middle term, 40np, matches 2ab. Calculate 2(5n)(4p) = 40np, which confirms it's a perfect square trinomial.
4. Write the factored form using the square roots: (5n + 4p)².
Therefore, the factored form of 25n² + 40np + 16p² is (5n + 4p)².
