Question

MULTIPLY
I AM A 9TH STUDENT I HAVEN'T STUDY MONDAY IS LAST DAY TO SUBMIT ​

Answer 1

Given :

•Multiply :

$\bf \: (a) \: ( \sqrt{2} + \sqrt{3})(2 \sqrt{3} + 5 \sqrt{6} )$

$\bf \: (b)(6 \sqrt{2} - 5 \sqrt{6} )(6 \sqrt{5} - 7 \sqrt{3} )$

To Find :

•Multiplication of the given values=?

Formulas :

$\bullet \bf \: ( {a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$

$\bf \bullet( {a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab$

$\bullet \bf \: {a}^{2} - {b}^{2} = (a + b)(a - b)$

$\bullet \bf \: {a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab$

Solution :

$\bf \: (a) \: ( \sqrt{2} + \sqrt{3})( 2 \sqrt{3} + 5 \sqrt{6} )$

Multiplying both sides :

$\\ \implies \displaystyle \sf \: \sqrt{2} (2 \sqrt{3} + 5 \sqrt{6} ) + \sqrt{3}(2 \sqrt{3} + 5 \sqrt{6} )$

$\\ \implies \sf \: 2 \sqrt{6} + 5 \sqrt{12} + 2 \sqrt{3 \times 3} + 5 \sqrt{18}$

$\\ \implies \sf \: 2 \sqrt{6} + 5 \times 2 \sqrt{3} + 6 + 5 \times 3 \sqrt{2}$

$\implies \sf \: 2 \sqrt{6} + 10 \sqrt{3} + 6 + 15 \sqrt{2}$

$\\ \implies\boxed{ \bf{2 \sqrt{6} + 10 \sqrt{3} + 6 + 15 \sqrt{2} }}$

$\bf \: (b) \: (6 \sqrt{2} - 5 \sqrt{6} )(6 \sqrt{5} - 7 \sqrt{3} )$

Multiplying both sides :

$\\ \implies \sf 6 \sqrt{2} (6 \sqrt{5} - 7 \sqrt{3} ) - 5 \sqrt{6} (6 \sqrt{5} - 7 \sqrt{3} )$

$\\ \implies \sf \: 36 \sqrt{10} - 42 \sqrt{6} - 30 \sqrt{30} + 35 \sqrt{18}$

$\\ \implies \sf \: 36 \sqrt{10} - 42 \sqrt{6} - 30 \sqrt{30} + 35 \times 3 \sqrt{2}$

$\\ \implies \boxed{ \bf{36 \sqrt{10} - 42 \sqrt{6} - 30 \sqrt{30} + 105 \sqrt{2} }}$