Question

Simplify
$(4 \sqrt{3 } - 2 \sqrt{2} )(4 \sqrt{3} + 2 \sqrt{2} )$
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Answer 1

$(4 \sqrt{3} - 2 \sqrt{2} )(4 \sqrt{3} + 2 \sqrt{2} ) \\ using \: \: {a}^{2} - {b}^{2} = (a - b)(a + b) \\ = ( {4 \sqrt{3} })^{2} - ( {2 \sqrt{2} })^{2} \\ = 16 \times 3 - 4 \times 2 \\ = 48 - 8 \\ = 40$

Answer 2

Answer :

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

By using identity :

• (a - b)(a + b) = a² - b²

$\sf : \implies (4 \sqrt{3 } - 2 \sqrt{2} )(4 \sqrt{3} + 2 \sqrt{2} )= (4)^2 - (2\sqrt{2})^2$

$\sf : \implies (4 \sqrt{3 } - 2 \sqrt{2} )(4 \sqrt{3} + 2 \sqrt{2} )= 16 - 4 \times 2$

$\sf : \implies (4 \sqrt{3 } - 2 \sqrt{2} )(4 \sqrt{3} + 2 \sqrt{2} )= 16 - 8$

$\sf : \implies (4 \sqrt{3 } - 2 \sqrt{2} )(4 \sqrt{3} + 2 \sqrt{2} )= 8$

Hence, Answer is 8.