which is the completely factored form of $4x^{2}+28x + 49$?\n$(x + 7)(4x + 7)$\n$4(x + 7)(x + 7)$\n$(2x +…

Explanation:

Step1: Identify the form

The expression $4x^{2}+28x + 49$ is in the form of $a^{2}+2ab + b^{2}$, where $a = 2x$ ($a^{2}=4x^{2}$ so $a=\sqrt{4x^{2}} = 2x$) and $b = 7$ ($b^{2}=49$ so $b=\sqrt{49}=7$ and $2ab=2\times(2x)\times7 = 28x$).

Step2: Apply the perfect - square formula

The perfect - square formula is $a^{2}+2ab + b^{2}=(a + b)^{2}$. Substituting $a = 2x$ and $b = 7$ into the formula, we get $(2x+7)^{2}=(2x + 7)(2x + 7)$.

Answer:

C. $(2x + 7)(2x + 7)$