Question

Simplify :

$\sf a) \: (2 \sqrt{2} - \sqrt{3} )(2 \sqrt{2} + 3)$

$\sf b) \: (4 \sqrt{6} - 2 \sqrt{7} )(4 \sqrt{6} + 7)$

Please Do It !
​

Answer 1

Given :-

$\sf a) \: (2 \sqrt{2} - \sqrt{3} )(2 \sqrt{2} + 3)$

$\sf b) \: (4 \sqrt{6} - 2 \sqrt{7} )(4 \sqrt{6} + 7)$

Solution :-

First Take one number and multiply with whole then take another and also multiply with whole.

→$(a + b) ( a - c)$

→$a ( a -c) +b (a-c)$

→$a^2 -ac + ab - bc$

Now, the given values are just like this form,

1)

→$( 2\sqrt{2} - \sqrt{3} )(2\sqrt{2}+3 )$

→$2\sqrt{2}(2\sqrt{2} + 3)-\sqrt{3}(2\sqrt{2} + 3)$

→$(2\sqrt{2})^2 + 3(2\sqrt{2}) - \sqrt{3} (\times 2\sqrt{2})- \sqrt{3}(3)$

→ $\boxed{\sf\red{ 8 + 6\sqrt{2} - 2\sqrt{6}-3\sqrt{3}}}$

Now,

2)

→$\sf b) \: (4 \sqrt{6} - 2 \sqrt{7} )(4 \sqrt{6} + 7)$

→$4\sqrt{6}(4\sqrt{6}+7) -2\sqrt{7}(4\sqrt{6}+7)$

→$(4\sqrt{6}^2 ) + 4\sqrt{6}(7) -2\sqrt{7}(4\sqrt{6} ) -2\sqrt{7}(7)$

→ $\boxed{\sf\red{ 96 + 28\sqrt{6} - 8\sqrt{42}-14\sqrt{7}}}$

Answer 2

Explanation:

Given Problem:

$\sf a)\: (2\sqrt{2} - \sqrt{3})\:(2\sqrt{2} + 3)$

$\sf b)\:(4\sqrt{6} - 2\sqrt{7})\:(4\sqrt{6} +7)$

Solution:

The step 1 is:

Take one number and multiply with whole then take another and also multiply with whole.

$\implies\ (a+b)(a-c)$

$a(a-c)+b(a-c)$

$a^2-ac+ab-bc$

Now,

Do same (form) with given values:

$\sf a)\: (2\sqrt{2} - \sqrt{3})\:(2\sqrt{2} + 3)$

$\implies\ 2\sqrt{2}(2\sqrt{2}+3) - \sqrt{3}   (2\sqrt{2}+3)$

$\implies\ (2\sqrt{2})^2+3(2\sqrt{2} ) -\sqrt{3} (\times2\sqrt{2)}- \sqrt{3}(3)$

$\implies\ \sf 8+6\sqrt{2} -2\sqrt{6}- 3 \sqrt{3}$

Now,

$\sf b)\:(4\sqrt{6} - 2\sqrt{7})\:(4\sqrt{6} +7)$

$\implies\ 4 \sqrt{6}(4 \sqrt {6}+7)-2\sqrt{7}(4 \sqrt {6} +7)$

$\implies\ (4 \sqrt{6}^2) + 4\sqrt{6}(7) - 2 \sqrt{7}(4 \sqrt {6}) -2 \sqrt{7}(7)$

$\sf 96+28 \sqrt {6}-8 \sqrt {42}-14 \sqrt{7}$