Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

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What does the expression (a+b)(c+d) expand to?

ac+ad+bc+bd
ab+ac
-b±[√b²-4ac]/2a
(a-b)(a²+ab+b²)

The correct answer is: ac+ad+bc+bd

The expression (a+b)(c+d) expands to ac + ad + bc + bd because of the distributive property, also known as the FOIL method in the context of binomials. When you distribute each term in the first set of parentheses (a + b) with each term in the second set of parentheses (c + d), you multiply as follows: 1. Multiply 'a' by 'c', resulting in 'ac'. 2. Multiply 'a' by 'd', resulting in 'ad'. 3. Multiply 'b' by 'c', resulting in 'bc'. 4. Multiply 'b' by 'd', resulting in 'bd'. Combining all these products gives you the complete expansion: ac + ad + bc + bd. This process showcases how two binomials can be expanded into a sum of products. The other choices do not represent the result of expanding (a+b)(c+d) through this method, highlighting the unique nature of the correct answer.