What must be added to b2-3ab to make it a perfect square?

The expression is probably b² - 3ab (the "b2" is b squared). We need to complete the square in b.

Concept: To complete the square for x² + px, add (p/2)².

Solution:

Treat the expression as b² - 3ab, where the coefficient of b is -3a.

Half of this coefficient is -3a/2, and squaring it gives:

(-3a/2)² = 9a²/4

Check: b² - 3ab + 9a²/4 = (b - 3a/2)², which is a perfect square.

Comparing with the options:

• A. -3a: no
• B. -3/2: no
• C. 9/4: this is missing a², so it only works if a = 1
• D. 9a/4: this has a instead of a², so it is wrong
• E. 9²/4: this is most likely a typo for 9a²/4, where the "a" was lost and the "2" became a superscript on the 9

The correct term is 9a²/4. Option E is written as 9²/4, which would equal 81/4 if read literally. That is not correct mathematically. But it is the option that most closely matches 9a²/4, since the "2" is in the squared position and the "a" appears to have been dropped in formatting.

Note: Read literally, none of the options is exactly right, so E is the intended answer because of a printing error in the option.

Tip: To complete the square, take half the middle coefficient and square it. Here the coefficient includes the letter a, so the "a" must be squared too, giving a².