(4\\sqrt{7}+3)(6\\sqrt{7}-1)
(4\\sqrt{7}+3)(6\\sqrt{7}-1)
Answer
Explanation:
Step1: Use the FOIL method
$$(4\sqrt{7}+3)(6\sqrt{7} - 1)=4\sqrt{7}\times6\sqrt{7}+4\sqrt{7}\times(- 1)+3\times6\sqrt{7}+3\times(-1)$$
Step2: Simplify each term
- For (4\sqrt{7}\times6\sqrt{7}): (4\times6\times(\sqrt{7}\times\sqrt{7}) = 24\times7=168)
- For (4\sqrt{7}\times(-1)): (-4\sqrt{7})
- For (3\times6\sqrt{7}): (18\sqrt{7})
- For (3\times(-1)): (-3)
So the expression becomes (168-4\sqrt{7}+18\sqrt{7}-3)
Step3: Combine like - terms
Combine the constant terms (168 - 3=165) and the radical terms (-4\sqrt{7}+18\sqrt{7}=14\sqrt{7})
Answer:
(165 + 14\sqrt{7})