Question

Simplify the following expressions:

a) (2+√3) (2+√2)

b) (√3-√2) (√3+√2)​

Answer 1

$\large\bf\underline\red{Answer \: :-}$

a) (2 + √3) (2 + √2)

$\sf\longrightarrow{2(2 + \sqrt{2} ) + \sqrt{3}(2 + \sqrt{2} ) } \\ \\ \sf\longrightarrow{4 + 2 \sqrt{2} + 2 \sqrt{3} + \sqrt{6} } \: \: \: \: \: \:$

Answer is 4 + 2√2 + 2√3 + √6

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b) (√3 - √2) (√3 + √2)

Using formula : (a+b) (a-b) = a² - b²

$\sf\longrightarrow{( \sqrt{3}) {}^{2} - ( \sqrt{2} ) {}^{2} } \\ \\ \sf\longrightarrow{3 - 2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf\longrightarrow \red{1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Answer is 1

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Important formulas

$\begin{gathered}\boxed{\begin{array}{c} \\ \tiny\bf{\dag}\:\underline{\frak{\rm{S}\frak{ome\:important\:algebric\:identities\:::}}} \\\\ \green{\bigstar}\:\rm \red{ (A+B)^{2} = A^{2} + 2AB + B^{2}} \\\\ \red{\bigstar}\rm\: \green{(A-B)^{2} = A^{2} - 2AB + B^{2}} \\\\ \orange{\bigstar}\rm\: \blue{A^{2} - B^{2} = (A+B)(A-B)}\\\\ \blue{\bigstar}\rm\: \orange{(A+B)^{2} = (A-B)^{2} + 4AB}\\\\ \pink{\bigstar}\rm\: \purple{(A-B)^{2} = (A+B)^{2} - 4AB}\\\\ \purple{\bigstar} \rm\: \pink{(A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}}\\\\ \pink{\bigstar}\rm\:(A-B)^{3} = A^{3} - 3AB(A-B) - B^{3}\\\\ \bigstar\rm\: \red{A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})} \\\\ \end{array}}\end{gathered}$

Answer 2

Answer:

a) 2(2+√2)+√3(2+√2)

4 + 2√2 + 2√3 + √6

b)