Question

Câu 1: Sử dụng hằng đẳng thức để rút gọn: 𝑎) 𝑥 3 + 64 𝑏) (𝑥 − 2) 3 + (𝑥 + 1) 3 𝑐) (3𝑥 + 4)(9𝑥 2 − 12𝑥 + 16)

Answer 1

a) x³ + 64 = x³ + 4³ = x³ + 4³ = (x + 4) (x² - 64x + 16) 

b) (x - 2)³ + (x + 1)³ = x³ - 3.x².2 + 3.x.2² - 2³ + x³ + 3.x².1 + 3.x.1² + 1³

= x³ - 6x² + 12x - 8 + x³ + 3x² + 3x + 1

= x⁶ - 3x⁴ + 15x² - 7

c)(3x + 4) (9x² - 12x + 16) = (3x + 4) [(3x)² - 3x.4 + 4²] = 3x³ + 4²

Answer 2

a)  x^3 + 64= x^3 + 4^3= (x+4) (x^2- x.4 + 4^2)= (x+4) (x^2- 4x +16)

b) (x-2)^3 + (x-1)^3= (x^3 – 3.x^2.2 +3.x.2^2 - 2^3)+(x^3 – 3.x^2.1 +3.x.1^2 – 1^3)

= (x^3 – 6x^2 + 12x – 8)+(x^3 – 3x^2+ 3x -1 )

= x^3 - 6x^2 + 12x – 8+ x^3 – 3x^2+ 3x -1

=2x^3 – 9x^2+ 15x – 9

c)   (3𝑥 + 4)(9𝑥^2 − 12𝑥 + 16)= (3x+4) [(3x)^2 – 3x.4 + 4^2]= (3x)^3 + 4^3