Cours Développer, identitiés remarquables

Exercice - Égalités remarquables, niveau moyen

L'énoncé

Développez, réduisez et ordonnez :


Question 1

\(A = \left(\dfrac{3}{5} x+5\right)^2\)

\(A =\left(\dfrac{3}{5}x\right)^2 +2\times \dfrac{3}{5}x \times 5+25\)
\(A =\dfrac{9}{25}x ^2 +6x +25\)

Question 2

\(B = \left(3x-\dfrac{1}{7}\right)^2\)

\(B = 9x^2-\dfrac{6}{7}x +\dfrac{1}{49}\)

Question 3

\(C = (-2x-9)^2 + (4x+1)^2\)

\(C = ((-1)(2x+9))^2 + (4x+1)^2\)

\(C = (-1)^2\times (2x+9)^2 + (4x+1)^2\)
Or \((-1)^2=1\),
Ainsi :

\(C = (2x+9)^2 + (4x+1)^2\)
\(C = 4x^2+36x +81 +16 x^2+8x+1\)
\(C =20x^2+44x +82 \)

Question 4

\(D = (-70x-8)(-70x+8)\)

\(D = (-70x)^2-8^2\)
\(D =4900 x^2-64\)

Question 5

\(E = (-6-11x)(6-11x)\)

On permute l'ordre des termes dans chaque parenthèse :
\(E = (-11x-6)(-11x+6)\)
\(E = (-11x)^2-6^2\)
\(E =121x^2-36\)