Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

The expanded form of (a - b)² is derived from the algebraic identity for the square of a binomial. When you expand (a - b)², you apply the formula (x - y)² = x² - 2xy + y², where x is a and y is b.

For (a - b)², substitute x with a and y with b:

1. Start by squaring the first term: a².

2. Then, multiply the two terms together and double the result: -2ab (since you are combining -a and -b).

3. Finally, square the second term: b².

Combining these, you arrive at the expression a² - 2ab + b², which precisely matches the first answer choice given.

The other options do not accurately reflect the expansion of (a - b)²:

- The second choice presents a² + 2ab + b², which incorrectly adds instead of subtracts the cross-product term.

- The third choice, (a - b)(a + b), is a product of sums and differences but does not reflect the expanded form.

- The last option, which includes a formula related to quadratic equations