Question

simplify the following expressions (2√3+√2)(2√3-√2)​

Answer 1

AnswEr:-

Your Answer Is 10.

ExplanaTion:-

Given expression:-

$\tt\longrightarrow(2 \sqrt{3} + \sqrt{2} )(2 \sqrt{3} - 2).$

So we have to simplify the given expression.

ID Used:-

$\tt\longrightarrow(a + b)( a - b) = { a}^{2} - b {}^{2} .$

Se let us simplify the given expression:-

$\tt\mapsto(2 \sqrt{3} + \sqrt{2})(2 \sqrt{3} - \sqrt{2} ). \\ \\ \tt = (2 \sqrt{3}) {}^{2} - ( \sqrt{2} ) {}^{2}. \\ \\ \tt(by \: \: using \: \: id). \\ \\ \tt = (2 \times 2 \times \sqrt{3} \times \sqrt{3} ) - ( \sqrt{2} \times \sqrt{2} ). \\ \\ \tt = (4 \times 3) - (2). \\ \\ \tt = 12 - 2. \\ \\ \tt = 10.$

$\tt\therefore$ The required answer is 10.

$\rule{200}2$

More Algebraic IDs:-

$\tt\longrightarrow(x + y) {}^{2} = {x}^{2} + 2xy + {y}^{2} . \\ \\ \tt\longrightarrow(x - y) {}^{2} = {x}^{2} - 2xy + {y}^{2} . \\ \\ \tt\longrightarrow(x + a)(x + b) = {x}^{2} + (a + b)x + ab. \\ \\ \tt\longrightarrow {x}^{2} + {y}^{2} = (x + y) {}^{2} - 2xy.$

$\rule{200}2$