Question

Expand and simplify (4 + 2)(6-12) Give your answer in the form b+cV2

Answer 1

Note: Consider the expression is $(4+\sqrt{2})(6-\sqrt{2})$.

Given:

$(4+\sqrt{2})(6-\sqrt{2})$

To find:

The value of given expression in the form of $b+c\sqrt{2}$.

Solution:

We have,

$(4+\sqrt{2})(6-\sqrt{2})$

Using distributive property, we get

$=4(6-\sqrt{2})+\sqrt{2}(6-\sqrt{2})$

$=4(6)+4(-\sqrt{2})+\sqrt{2}(6)+\sqrt{2}(-\sqrt{2})$

$=24-4\sqrt{2}+6\sqrt{2}-2$

On combining like terms, we get

$=(24-2)+(6\sqrt{2}-4\sqrt{2})$

$=22+2\sqrt{2}$

On comparing with $b+c\sqrt{2}$, we get

$a=22,b=2$

Therefore, the required form is $22+2\sqrt{2}$.