Question

which of the following expressions are perfect-square trinomials? check all of the boxes that apply.\\(\square\\) \\(x^2 - 16x - 64\\)\\(\square\\) \\(4x^2 + 12x + 9\\)\\(\square\\) \\(x^2 + 20x + 100\\)\\(\square\\) \\(x^2 + 4x + 16\\)done

Explanation:

Step1: Recall perfect-square form

A perfect-square trinomial follows $a^2\pm2ab+b^2=(a\pm b)^2$.

Step2: Test $x^2-16x-64$

Last term is negative, can't be $b^2$. Reject.

Step3: Test $4x^2+12x+9$

$4x^2=(2x)^2$, $9=3^2$, $2ab=2(2x)(3)=12x$. Matches.

Step4: Test $x^2+20x+100$

$x^2=x^2$, $100=10^2$, $2ab=2(x)(10)=20x$. Matches.

Step5: Test $x^2+4x+16$

$2ab=2(x)(4)=8x
eq4x$. Reject.

Answer:

$4x^2 + 12x + 9$, $x^2 + 20x + 100$