Question

which of the following is a perfect square trinomial?
a. 4x² + 14xy - 25y²
b. 4x² + 20xy - 25y²
c. 4x² - 14xy + 25y²
d. 4x² - 20xy + 25y²

Explanation:

Step1: Recall perfect - square trinomial formula

A perfect - square trinomial is of the form $(a\pm b)^2=a^{2}\pm2ab + b^{2}$.

Step2: Analyze option D

For the trinomial $4x^{2}-20xy + 25y^{2}$, we can rewrite it as $(2x)^{2}-2\times(2x)\times(5y)+(5y)^{2}$. Here, $a = 2x$ and $b = 5y$, and it follows the form $(a - b)^2$.

Step3: Analyze other options

• Option A: $4x^{2}+14xy-25y^{2}$ does not follow the form $a^{2}\pm2ab + b^{2}$ as the last term is negative and the middle - term does not match the $2ab$ form for the first and third terms.
• Option B: $4x^{2}+20xy-25y^{2}$ does not follow the form $a^{2}\pm2ab + b^{2}$ as the last term is negative.
• Option C: $4x^{2}-14xy + 25y^{2}$, the middle - term $-14xy$ does not match the $2ab$ form for $a = 2x$ and $b = 5y$ ($2ab=2\times(2x)\times(5y)=20xy$).

Answer:

D. $4x^{2}-20xy + 25y^{2}$