Exercice 1
Développer et réduire : \(A = (x + 3)(2x - 1)\) ; \(B = -3(2 - x) + x(x + 1)\).
Correction
\(A = 2x^2 - x + 6x - 3 = 2x^2 + 5x - 3\). \(B = -6 + 3x + x^2 + x = x^2 + 4x - 6\).
Exercice 2
Développer à l'aide des identités : \((x + 6)^2\) ; \((2x - 5)^2\) ; \((3x + 1)(3x - 1)\) ; \(\left(x - \frac12\right)^2\).
Correction
\(x^2 + 12x + 36\) ; \(4x^2 - 20x + 25\) ; \(9x^2 - 1\) ; \(x^2 - x + \frac14\).
Exercice 3
Factoriser : \(C = 5x^2 - 10x\) ; \(D = x^2 - 25\) ; \(E = x^2 + 8x + 16\) ; \(F = 9x^2 - 4\).
Correction
\(C = 5x(x - 2)\) ; \(D = (x - 5)(x + 5)\) ; \(E = (x + 4)^2\) ; \(F = (3x - 2)(3x + 2)\).
Exercice 4
Factoriser : \(G = (2x + 1)(x - 3) - (2x + 1)(4x + 2)\).
Correction
\(G = (2x + 1)[(x - 3) - (4x + 2)] = (2x + 1)(-3x - 5)\).
Exercice 5
Calculer mentalement : \(99^2\) ; \(51\times49\).
Correction
\(99^2 = (100 - 1)^2 = 10\,000 - 200 + 1 = 9801\). \(51\times49 = (50 + 1)(50 - 1) = 2500 - 1 = 2499\).