Question 21

9a² - 12ab + 4b²

To simplify the expression (3a - 2) ^ 2, we can apply the square of a binomial formula, resulting in 9a² - 12ab + 4b².

A) 9a²-4b2

This option is incorrect because it does not account for the middle term that arises from squaring the binomial. The correct expansion must include a term that represents the product of the two terms multiplied by 2.

B) 9a²+4b^2

This option is also incorrect. While it correctly identifies the squares of the individual terms, it mistakenly adds them together instead of including the necessary middle term that is crucial in the expansion of a binomial.

C) 9a^2-6ab-4b^2

This option is incorrect as it has the wrong coefficients and signs. The middle term (-6ab) is not derived from the proper calculation of the binomial expansion, and the constant term (-4b^2) is incorrect in both sign and value.

D) 9a^2-6ab+4b^2

This choice is incorrect because, although it has the correct first and last terms, the middle term (-6ab) is not accurate. The correct coefficient for the middle term should be -12, not -6, which is essential for the accurate expansion of the binomial.

E) 9a² - 12ab +4b²

This option is correct as it accurately reflects the expansion of (3a - 2) ^ 2 using the formula (x - y)² = x² - 2xy + y², yielding the terms 9a², -12ab, and 4b².

Conclusion

The correct answer, 9a² - 12ab + 4b², stems from the proper application of the binomial expansion. All other options fail due to incorrect coefficients or omissions of necessary terms, highlighting the importance of accurately following algebraic rules when expanding expressions.