Multiplying Radical Expressions with Multiple Terms
Multiplying radical expressions with multiple terms uses the Distributive Property — exactly as with polynomial multiplication. In Grade 11 enVision Algebra 1 (Chapter 9: Solving Quadratic Equations), students distribute each term in the first expression to each term in the second, then simplify any resulting radicals and combine like terms. For example, (√3 + 2)(√3 − 5) requires distributing to get 4 terms, simplifying √3 · √3 = 3, and combining like radical terms. The FOIL method applies when both factors are binomials.
Key Concepts
To multiply radical expressions with multiple terms, use the Distributive Property. Distribute each term in the first expression to each term in the second expression, then simplify any resulting radicals.
Common Questions
How do you multiply radical expressions with multiple terms?
Apply the Distributive Property: multiply each term in the first expression by each term in the second, then simplify radicals and combine like terms.
Can you use FOIL to multiply radical binomials?
Yes. For two binomials like (√a + b)(√c + d), FOIL works: First, Outer, Inner, Last — same process as polynomial multiplication.
What is the product of (√5)(√5)?
√5 · √5 = √25 = 5. Multiplying a square root by itself gives the radicand.
How do you simplify √12 after multiplying radicals?
Factor the radicand: √12 = √(4 · 3) = 2√3. Always simplify radicals in your final answer.
What are like radical terms?
Like radical terms have the same radicand: 3√2 and 5√2 are like terms and can be combined to give 8√2.
Can you multiply (√3 + 2)(√3 − 2)?
Yes. This is a difference of squares pattern: (√3)² − 2² = 3 − 4 = −1.