# How do you know if 100a^2 + 100a + 25 is a perfect square trinomial and how do you factor it?

May 19, 2018

${\left(10 a + 5\right)}^{2}$

#### Explanation:

For a prefect square trinomial. look for the following properties,

First and third terms must be perfect squares.

$\sqrt{100 {a}^{2}} = 10 a \text{ } \mathmr{and} \sqrt{25} = 5$

Check whether the middle term is the product of the two square roots, doubled.

$10 a \times 5 = 50 a \text{ } \rightarrow 2 \times 50 a = 100 a$

If these properties are present the trinomial is a perfect square.

To factorise:

$100 {a}^{2} + 100 a + 25$

The binomial is made up of:

• square root of the first term $\left(10 a\right)$
• the sign of the second term $\left(+\right)$
• the square root of the third term $5$

$= {\left(10 a + 5\right)}^{2}$