Question

Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.

$\mathbf{4}{x}^2-\mathbf{20}x+\mathbf{25}$

Short answer

Yes, the factor of a given trinomial is $\left(\mathbf{2}x-\mathbf{5}\right)\left(\mathbf{2}x-\mathbf{5}\right)$.

Step-by-step solution

Step 1. Check.

Check whether the given trinomial is a perfect square or not.

Here, the first term is $4x^2={\left(2x\right)}^2$.

Middle term is $20x=2\left(2x\right)\left(5\right)$, which is in the form of $2ab$.

The last term is $25=5^2$.

So, the given trinomial is a perfect square.

Step 2. Factor the trinomial.

Factor the perfect square trinomial.

$4x^2-10x-10x+25=2x\left(x-5\right)-5\left(2x-5\right)$

Step 3. Simplify.

Simplify the above-obtained expression.

$\left(2x-5\right)\left(2x-5\right)$

Therefore, the factor $4x^2-20x+25$is $\left(2x-5\right)\left(2x-5\right)$.