Example Card: Multiplying Binomials with Radicals
Multiply binomials containing radical terms using FOIL, then combine like radical terms and simplify. Practice Grade 9 radical expression multiplication.
Key Concepts
You already know how to FOIL binomials. Let's apply that same skill to expressions with radicals, a key idea from this lesson.
Example Problem Simplify the expression $(5 + \sqrt{2})(3 \sqrt{8})$.
Step by Step 1. Use the FOIL method (First, Outer, Inner, Last) to multiply the binomials. $$ \underbrace{(5)(3)} {\text{First}} + \underbrace{(5)( \sqrt{8})} {\text{Outer}} + \underbrace{(\sqrt{2})(3)} {\text{Inner}} + \underbrace{(\sqrt{2})( \sqrt{8})} {\text{Last}} $$ 2. Calculate each product. $$ 15 5\sqrt{8} + 3\sqrt{2} \sqrt{16} $$ 3. Simplify any radicals. We can simplify $\sqrt{8}$ and $\sqrt{16}$. $$ \sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2} $$ $$ \sqrt{16} = 4 $$ 4. Substitute these simplified forms back into the expression. $$ 15 5(2\sqrt{2}) + 3\sqrt{2} 4 $$ $$ 15 10\sqrt{2} + 3\sqrt{2} 4 $$ 5. Combine like terms: group constants and radical terms. $$ (15 4) + ( 10\sqrt{2} + 3\sqrt{2}) = 11 7\sqrt{2} $$.
Common Questions
What is Multiplying Binomials with Radicals in Grade 9 algebra?
It is a core concept in Grade 9 algebra that builds problem-solving skills and prepares students for advanced math coursework.
How do you apply multiplying binomials with radicals to solve problems?
Identify the relevant formula or property, substitute known values carefully, apply each step in order, and verify the result makes sense.
What common errors occur with multiplying binomials with radicals?
Misapplying the rule to wrong scenarios, sign mistakes, and forgetting to check answers in the original problem.