Giải thích các bước giải:
a/. (x + 4)(x² - 4x + 16)
= (x + 4)(x² - x. 4x + 4²)
= x³ + 4³
= x³ + 64
b/. (x + y)² - (x - y)²
= [(x + y) - (x - y)][(x + y) + (x - y)]
= (x + y - x + y)(x + y + x - y)
= 2y . 2x
= 4xy
c/. (x + y)³ - (x + y)(x² - xy + y²)
= x³ + 3x²y + 3xy² + y³ - (x³ + y³)
= (x³ - x³) + 3x²y + 3xy² + (y³ - y³)
= 3x²y + 3xy²
= 3xy(x + y)
d/. (x - 2)(x² + 2x + 4) - 6x² + 12x
= (x - 2)(x² + 2x + 4) - 6x(x - 2)
= (x - 2)[(x² + 2x + 4) - 6x]
= (x - 2)(x² + 2x + 4 - 6x)
= (x - 2)(x² - 4x + 4)
= (x - 2)(x - 2)²
= (x - 2)³
e/. (2x + 5)(5 - 2x) + (x - 5)(5 + 4x)
= (2x + 5)-(2x - 5) + 5x + 4x² - 25 - 20x
= - [(2x)² - 5²] + 4x² - 25 + (5x - 20x)
= - 4x² + 25 + 4x² - 25 - 15x
= (- 4x²+ 4x²) + (25 - 25) - 15x
= - 15x
f/. 4x² + 4x + 1 - (2x - 1)²
= [(2x)² + 2. 2. x + 1] - (2x - 1)²
= (2x + 1)² - (2x - 1)²
= [2x + 1 - (2x - 1)](2x + 1 + 2x - 1)
= (2x + 1 - 2x + 1)[(2x + 2x)(1 - 1)]
= 2. 4x
= 8x
g/. (x + 5)(x² + 5x + 25) - 10x(x + 5) - x³
= x³ + 5x² + 25x + 5x² + 25x + 125 - 10x² - 50x - x³
= (x³- x³) + (5x²+ 5x² - 10x²) + (25x + 25x - 50x) + 125
= 125
Chúc bạn học tốt nhé
