Bài 7:
a. A = (2x + 3y)² - 2(2x - y)²
= (4x² + 12xy + 9y²) - 2(4x² - 4xy + y²)
= (4x² + 12xy + 9y²) - (8x² - 8xy + 2y²)
= 4x² + 12xy + 9y² - 8x² + 8xy - 2y²
= -4x² + 20xy + 7y²
b. B = 16(x + y)(x - y) - (4x - 3)²
= 16(x² - y²) - (16x² - 24x + 9)
= 16x² - 16y² - 16x² + 24x - 9
= -16y² + 24x - 9
c. C = (2x + 3)³ - 8x²(x + 1) + 1
= [(2x + 3)³ + 1] - 8x²(x + 1)
= [(2x + 3) + 1][(2x + 3)² - (2x + 3).1 + 1²] - (8x³ + 8x²)
= (2x + 3 + 1)(4x² + 12x + 9 - 2x - 3 + 1) - (8x³ + 8x²)
= (2x + 4)(4x² + 10x + 7) - (8x³ + 8x²)
= (8x³ + 20x² + 14x + 16x² + 40x + 28) - (8x³ + 8x²)
= 8x³ + 20x² + 14x + 16x² + 40x + 28 - 8x³ - 8x²
= 28x² + 54x + 28
d. D = (2x + 1)³ - 4(x - 2)³
= (8x³ + 12x² + 6x + 1) - 4(x³ - 6x² + 12x - 8)
= (8x³ + 12x² + 6x + 1) - (4x³ - 24x² + 48x - 32)
= 8x³ + 12x² + 6x + 1 - 4x³ + 24x² - 48x + 32
= 4x³ + 36x² - 42x + 33
Bài 6:
a. (3x - 5)(9x² + 15x + 25)
= (3x - 5)[(3x)² + 3x.5 + 5²)
= (3x)³ - 5³
= 27x³ - 125
b. (2x + 7)(4x² - 14x + 49) - 2x(2x - 1)(2x + 1)
= (2x + 7)[(2x)² - 2x.7 + 7²] - 2x[(2x)² - 1²]
= [(2x)³ + 7³] - 2x(4x² - 1)
= (8x³ + 343) - (8x³ - 2x)
= 8x³ + 343 - 8x³ + 2x
= 2x + 343
