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QUIZ
Identités remarquables (méthode)
Exercice n°1
On veut développer l'expression : $(-8y+x)^2$
Question 1 :
On reconnaît l'identité remarquable :
$(\color{}{a}+\color{}{b})(\color{}{a}-\color{}{b}) = a^2 - b^2$ $(\color{}{a}-\color{}{b})^2 = a^2 - 2\color{}a\color{}b + b^2$ $(\color{}{a}+\color{}{b})^2 = a^2 + 2\color{}a\color{}b + b^2$
Question 2 :
Ici $\color{red}a =$ ?
$-8\,y^2$ $-8y$ $64\,y^2$ $8y$
Question 3 :
Et $\color{green}b = $ ?
$\,x^2$ $-x$ $-\,x^2$ $x$
Question 4 :
$(\color{red}{-8y}+\color{green}{x})^2 \,$ $=\,(\color{red}{-8y})^2 \,+ 2\times\color{red}{(-8y\,)}\times\color{green}{x} \,+ \color{green}{x}^2$ $= $ ?
$-8\,y^2\, -16\,x\,y\,+ \,x^2$ $64\,y^2\, -16\,x\,y\,+ \,x^2$ $64y\, -16\,x\,y\,+ \,x^2$ $-64\,y^2\, -16\,x\,y\,+ \,x^2$
Exercice n°2
On veut développer l'expression : $(9x-y)^2$
$(\color{}{a}-\color{}{b})^2 = a^2 - 2\color{}a\color{}b + b^2$ $(\color{}{a}+\color{}{b})^2 = a^2 + 2\color{}a\color{}b + b^2$ $(\color{}{a}+\color{}{b})(\color{}{a}-\color{}{b}) = a^2 - b^2$
$9x$ $9\,x^2$ $-9x$ $81\,x^2$
$-y$ $y$ $-\,y^2$ $\,y^2$
$(\color{red}{9x}-\color{green}{y})^2 \,$ $=\,(\color{red}{9x})^2 \,- 2\times\color{red}{9x}\times\color{green}{y} \,+ \color{green}{y}^2$ $= $ ?
$9\,x^2\, -18\,x\,y\,+ \,y^2$ $81\,x^2\, -18\,x\,y\,- \,y^2$ $81\,x^2\, -18\,x\,y\,+ \,y^2$ $81x\, -18\,x\,y\,+ \,y^2$
Exercice n°3
On veut développer l'expression : $(-4x+7)(-4x-7)$
$(\color{}{a}-\color{}{b})^2 = a^2 - 2\color{}a\color{}b + b^2$ $(\color{}{a}+\color{}{b})(\color{}{a}-\color{}{b}) = a^2 - b^2$ $(\color{}{a}+\color{}{b})^2 = a^2 + 2\color{}a\color{}b + b^2$
$4x$ $-4\,x^2$ $-4x$ $16\,x^2$
$7$ $-49$ $49$
$(\color{red}{-4x}+\color{green}{7})(\color{red}{-4x}-\color{green}{7}) \,$ $=\,(\color{red}{-4x})^2 - \color{green}{7}^2$ $= $ ?
$-4\,x^2 \,- 49$ $16\,x^2 \,- 49$ $-16\,x^2 \,- 49$ $16\,x^2 \,+ 49$
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