Question

what values are needed to make each expression a perfect square trinomial?

• ( x^2 + 2x + square )
• ( x^2 - 20x + square )
• ( x^2 + 6x + square )

Explanation:

Step1: Recall perfect square formula

A perfect square trinomial follows $x^2 + 2bx + b^2=(x+b)^2$ or $x^2 - 2bx + b^2=(x-b)^2$. For $x^2+2x+\square$, identify $2b=2$.

Step2: Solve for $b$ and find $b^2$

$2b=2 \implies b=1$, so $b^2=1^2=1$.

Step3: For $x^2-20x+\square$, identify $2b=20$

$2b=20 \implies b=10$, so $b^2=10^2=100$.

Step4: For $x^2+6x+\square$, identify $2b=6$

$2b=6 \implies b=3$, so $b^2=3^2=9$.

Answer:

1. $1$
2. $100$
3. $9$