Question

rule and formulas alzebra

Answer 1

(a+b)2=a2+2ab+b2
(a)2+(b)2=(a+b)(a-b)
(a-b)2=a2-2ab+b2
(x+a) (x+b)=x2+(a+b)x+a*b

Answer 2

$\boxed{ \huge{ \color{blue} \frak{Formulas \: : }}}$

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$\pink{(x + a)(x + b) = {x}^{2} + (a + b)x + ab} \\ \\ = x(x + b) + a(x + b) \\ = {x}^{2} + xb + ax + ab \\ = {x}^{2} +bx +ax +ab \\ \bf= {x}^{2} + (a + b)x + ab$

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$\blue{(a + b) {}^{2} = {a}^{2} + 2ab + b {}^{2} } \\ \\ = (a + b) \times (a + b) \\ = a(a + b) + b(a + b) \\ = {a}^{2} + ab + ba + {b}^{2} \\ = {a}^{2} + ab + ab + {b}^{2} \\ \bf = a {}^{2} + 2ab + {b}^{2}$

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$\red{{(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} } \\ \\ = (a - b) \times (a - b) \\ = a(a - b) - b(a - b) \\ = {a}^{2} - ab - ba + {b}^{2} \\ = {a}^{2} - ab - ab + {b}^{2} \\ \bf= {a}^{2} - 2ab + {b}^{2}$

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