Question

Choose the correct answer.

Which one of the following trinomial is not a perfect square?

• A. $4a^2-6ab+9b^2$
• B. $4a^2+12ab+9b^2$
• C. $4a^2-12ab+9b^2$
• D. $-4a^2-12ab+9b^2$

Answer 1

Answer: (A), (D)

$-4a^2-12ab+9b^2$

Solving for Option (A)

Step 1: Find two terms which are complete square

$={\left(2a\right)}^2-6ab+{\left(3b\right)}^2$

Step 2: Now check if the middle term is in the form of $2ab$ where $a=2a$ and $b=3b$

$2ab=2\left(2a\right)\left(3b\right)=12ab$

The middle term given in the question is not equal to the term we obtained,

Hence, it is not a perfect square.

Solving for Option (B)

Step 1: Find two terms which are complete square

${\left(2a\right)}^2+12ab+{\left(3b\right)}^2$

Step 2: Now check if the middle term is in the form of $2ab$ where $a=2a$ and $b=3b$

$2ab=2\left(2a\right)\left(3b\right)=12ab$

The middle term given in the question is not equal to the term we obtained,

Hence, it is a perfect square.

Solving for Option (C)

Step 1: Find two terms which are complete square

${\left(2a\right)}^2-12ab+{\left(3b\right)}^2$

Step 2: Now check if the middle term is in the form of $2ab$ where $a=2a$ and $b=3b$

$2ab=2\left(2a\right)\left(3b\right)=12ab$

The middle term given in the question is equal to the term we obtained.

Hence, it is a perfect square.

Solving for Option (D)

Here, we don't have two complete square terms

Hence, it is a perfect square.

So, the correct options are (A) and (D)