1. Problem: Determine if $b^2 + 14b - 49$ is a perfect trinomial square. Step 1: Recall a perfect trinomial square has the form $$a^2 + 2ab + b^2 = (a+b)^2$$ or $$a^2 - 2ab + b^2 = (a-b)^2$$. Step 2: Check if $b^2 + 14b - 49$ fits this form. Step 3: The constant term should be a perfect square, but $-49$ is negative, so no. 2. Problem: Determine if $25x^4 - 60x^2y^2 + 36y^4$ is a perfect trinomial square. Step 1: Recognize $25x^4 = (5x^2)^2$, $36y^4 = (6y^2)^2$. Step 2: Check middle term: $-60x^2y^2 = 2 imes 5x^2 imes (-6y^2)$. Step 3: Matches form $(5x^2 - 6y^2)^2$, so yes. 3. Problem: Determine if $x^2 + 10x + 25$ is a perfect trinomial square. Step 1: $x^2 = (x)^2$, $25 = (5)^2$. Step 2: Middle term $10x = 2 imes x imes 5$. Step 3: Matches $(x + 5)^2$, so yes. 4. Problem: Determine if $c^2 - 2cd - d^2$ is a perfect trinomial square. Step 1: $c^2 = (c)^2$, $d^2 = (d)^2$. Step 2: Middle term $-2cd = 2 imes c imes (-d)$. Step 3: Matches $(c - d)^2$, so yes. 5. Problem: Determine if $81a^2 - 72ab + 16b^2$ is a perfect trinomial square. Step 1: $81a^2 = (9a)^2$, $16b^2 = (4b)^2$. Step 2: Middle term $-72ab = 2 imes 9a imes (-4b)$. Step 3: Matches $(9a - 4b)^2$, so yes. Final answers: 1. No 2. Yes 3. Yes 4. Yes 5. Yes