Bonjour
KLovht
a) x² + 3x = x(x + 3)
b) (3x + 1) - (3x + 1)(2x + 8) = (3x + 1)[1 - (2x + 8)]
= (3x + 1)(1 - 2x - 8)
= (3x + 1)(-2x - 7)
c) (x + 1)(2x + 21) + (2x + 2)(3 - x) = (x + 1)(2x + 21) + 2(x + 1)(3 - x)
= (x + 1)[(2x + 21) + 2(3 - x)]
= (x + 1)(2x + 21 + 6 - 2x)
= (x + 1) * 27
= 27(x + 1)
d) (2x + 3)² - (2x+ 3)(x + 7) = (2x + 3)(2x + 3) - (2x+ 3)(x + 7)
= (2x + 3)[(2x + 3) - (x + 7)]
= (2x + 3)(2x + 3 - x - 7)
= (2x + 3)(x - 4)
e) 4x² - 25 = (2x)² - 5²
= (2x + 5)(2x - 5)
f) x² - 7 = x² - (√7)²
= (x + √7)(x - √7)
g) 49x² + 14x + 1 = (7x)² + 2*(7x)*1 + 1²
= (7x + 1)²
h) (2 - x)(3x + 1) - (x - 2)(4x + 4) = (2 - x)(3x + 1) + (2 - x)(4x + 4)
= (2 - x)[(3x + 1) + (4x + 4)]
= (2 - x)(3x + 1 + 4x + 4)
= (2 - x)(7x + 5)
i) (x + 1)² - 2(x + 1)(2x + 3) + (2x + 3)² = [(x + 1) - (2x + 3)]²
= (x + 1 - 2x - 3)²
= (-x - 2)²
j) (4x² + 4x + 1) - (3x + 5)(2x + 1) = (2x + 1)² - (3x + 5)(2x + 1)
= (2x + 1)(2x + 1) - (3x + 5)(2x + 1)
= (2x + 1)[(2x + 1) - (3x + 5)]
= (2x + 1)(2x + 1 - 3x - 5)
= (2x + 1)(-x - 4)
