Question

Simplify (2V5 - 4)(3 V5+2). a. 4 c. b. 8-4v5 d. 22-8v5

Answer 1

Answer:

$(2\sqrt{5} - 4)(3\sqrt{5}+2)= 22 - 8\sqrt{5}$

Step-by-step explanation:

Given

$(2\sqrt{5} - 4)(3\sqrt{5}+2)$

Required

Simplify

$(2\sqrt{5} - 4)(3\sqrt{5}+2).$

Expand brackets

$2\sqrt{5}(3\sqrt{5}+2). - 4(3\sqrt{5}+2).$

Open each bracket

$2\sqrt{5}*3\sqrt{5}+2\sqrt{5}*2 - 4*3\sqrt{5}-4*2$

$6 * 5 + 4\sqrt{5} - 12\sqrt{5} - 8$

$30 + 4\sqrt{5} - 12\sqrt{5} - 8$

Collect Like Terms

$- 8+30 + 4\sqrt{5} - 12\sqrt{5}$

$22 - 8\sqrt{5}$

Hence:

$(2\sqrt{5} - 4)(3\sqrt{5}+2)= 22 - 8\sqrt{5}$