Question

please help i don't understand this complete the square to form a perfect square trinomial. then factor the trinomial.

Answer 1

The square of a binomial is:

(a + b)² = a² + 2ab + b²

The expression is

m² + 10m + __

which means that

a = m

and

2ab = 10m

ab = 5m

Replacing with a = m,

mb = 5m

b = 5

Then the factored expression is:

(m + 5)²

and the perfect square trinomial is:

(m + 5)² = m² + 2(5)m + 5² = m² + 10m + 25