(1 - 5x)² peut s'écrire (-5x + 1)² = (-(5x - 1))² = (5x -1)²
en utilisant les identités remarquables
(a - b)² = a² - 2ab + b²
a = 5x (5x -1)² = 25x² - 10x + 1
b = -1
2(5x)(-1) = -10x
(3 - 7x)(3 - 7x) = (3 - 7x)² = (-7x + 3)² = (-(7x - 3))² = (7x - 3)²
a = 7x
b = -3
2ab = 2(7x)(-3) = -42x
(7x - 3)² = 49x² - 42x ² + 9
(4 + 8x)² = (8x + 4)²
(a + b)² = a² + 2ab + b²
a = 8x
b = 4 ⇒ b² = 16
2ab = 2(8x)(4) = 64x
(8x + 4)² = 64x² + 64x + 16
(3 + 5a)(3 + 5a) = (5a + 3)²
a' = 5a
b = 3 ⇒b² = 9
2a'b = 2(5a)(3) = 30a
(5a + 3)² = 25a² + 30a + 9
(2 - 6x)(2 + 6x) = (-6x + 2)(6x + 2) = -(6x - 2)(6x +2) = - ((6x)² - 2²) = - 36x² + 4
a² - b² = (a + b)(a - b)
(1 - 5x)(1 + 5x) = -(5x -1)(5x + 1) = - ((5x)² - 1) = - 25x² + 1
(2 + 3x)(2 - 3x) - (5 - 2x)²
(2 + 3x)(2 - 3x) = -(3x -1)(3x + 1) = - ((3x)² - 1) = - 9x² + 1
(5 - 2x)² = (-(2x - 5))² = (2x - 5)²
(a - b)² = a² - 2ab + b²
a = 2x
b = -5 ⇒b² = 25
2ab = 2(2x)(-5) = -20x
(2x - 5)² = 4x² - 20x + 25
- 9x² + 1 - (4x² - 20x + 25)
- 9x² + 1 - 4x² + 20x - 25 = - 13x² + 20x - 24
(7 + x)² + (x - 5)(2x + 5)
(7 + x)² = (x + 7)² = x² + 14x + 49
(a + b)² = a² + 2ab + b²
a = x
b = 7 ⇒ b² = 49
2ab = 2(x)(7) = 14x
x² + 14x + 49 + (2x² + 5x - 10x - 25)
x² + 14x + 49 + 2x² + 5x - 10x - 25 = 3x² + 9x - 25