Question

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

$\mathbf{4}{x}^2+\mathbf{4}x+\mathbf{1}$

Short answer

Yes, the factor of given trinomial are $\left(\mathbf{2}x+\mathbf{1}\right)\left(\mathbf{2}x+\mathbf{1}\right)$.

Step-by-step solution

Step 1. Check.

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

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

Middle term is $4x=2\left(2x\right)\left(1\right)$, which is in the form of $2ab$.

Last term is $1^2=1$.

So, the given trinomial is a perfect square.

Step 2. Factor the trinomial.

Factor the perfect square trinomial.

$4x^2+2x+2x+1=2x\left(2x+1\right)+1\left(2x+1\right)$

Step 3. Simplify.

Simplify the above obtained expression.

$\left(2x+1\right)\left(2x+1\right)$

Therefore, the factor of$4x^2+4x+1$ are $\left(2x+1\right)\left(2x+1\right)$.