Question

(a + b) (a - b) = a2– b2​

Answer 1

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

$=>a(a - b) +b(a - b) ={a}^{2} - {b}^{2}$

$= > \: {a}^{2} - ab + ba - {b}^{2} = {a}^{2} - {b}^{2}$

$= > {a}^{2} - {b}^{2} - ab + ba = {a}^{2} - {b}^{2}$

$= > {a}^{2} - {b}^{2} = {a}^{2} - {b}^{2}$

Answer 2

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

$a(a - b) +b(a - b) ={a}^{2} - {b}^{2}$

$\: {a}^{2} - ab + ba - {b}^{2} = {a}^{2} - {b}^{2}$

${a}^{2} - {b}^{2} - ab + ba = {a}^{2} - {b}^{2}$

${a}^{2} - {b}^{2} = {a}^{2} - {b}^{2}$

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$\begin{gathered}\boxed{\begin{array}{| c |}\qquad\tt\large\textsf{ ! Formulas ! }\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{ ( a + b )² = a² + 2ab + b² }\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{ ( a - b )² = a² - 2ab + b² }\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{ a² - b² = ( a + b ) ( a - b ) }\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{ ( a + b )³ = a³ + 3a²b + 3ab² }\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{ ( a - b )³ = a³ - 3a²b + 3ab² - b³ }\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{ a³ - b³ = ( a - b ) ( a² + ab + b² ) }\end{array}}\end{gathered}$

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