Bài 1
a) -7x2. (x2y + 5x – 3)
= -7x2. x2y – 7x2. 5x – 7x2. (-3)
= -7x4y – 35x3 + 21x2
b) (2x + 3). (x2 – 4x + 1)
= 2x. (x2 – 4x + 1) + 3. (x2 – 4x + 1)
= 2x.x2 + 2x.(-4x) + 2x.1 + 3.x2 + 3.(-4x) + 3.1
= 2x3 – 8x2 + 2x + 3x2 – 12x + 3
= 2x3 + (-8x2 + 3x2) + (2x – 12x) + 3
= 2x3 – 5x2 – 10x + 3
Bài 2
a) 9x2y2 + 15x2y – 21xy2
= 3xy. (3xy + 5x – 7y)
b) x2 – 64
= x2 – 82
= (x + 8). (x – 8)
c) 5xy2 – 10xyz + 5xz2
= 5xy. (y – 2z + z2)
d) 3x2 – 12y2
= 3. (x2 – 4y2)
= 3. [x2 – (2y)2]
= 3. (x + 2y). (x – 2y)
e) y2. (x2 + y) – zx2 – zy
= y2. x2 + y2.y – zx2 – zy
f) x2 – 16 + 2xy + y2
= (x2 + 2xy + y2) – 16
= (x2 + 2.x.y + y2) – 16
= (x + y)2 – 42
= (x + y + 4). (x + y – 4)
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