BT DS8 full chuong 1

§ 1 NHÂN ĐƠN THỨC VỚI ĐA THỨC

Quy tắc: A(B + C) = AB + AC

VD: 1). 8x.( 3x3 – 6x +4 ) = 8x.3x3 +8x.( –6x) +8x.4= 24 x4 – 48x2 + 32x.
2). 2x2.(x2 + 5x –
) = 2x3.x2 + 2x3.5x – 2x3.
= 2x5 + 10x4 – x3.
3). ( 3x3y –
= 18x4 y4 – 3x3y3 +
x2y4.
4). (4x3 – 5xy + 2x) (–
xy) = –2x4 y +
x2y2 – x2y
Áp dụng: xn-1(x + y) –y(xn-1yn-1) = xn-1.x + xn-1.y – xn-1.y – y.yn-1 = xn-1+1 + xn-1.y – xn-1.y – y1+n+1


§ 2 NHÂN ĐA THỨC VỚI ĐA THỨC

Quy tắc: (A + B)(C + D) = AC + AD + BC + BD

VD: Tính
1). (x + 3)(x2 + 3x –5) = x3 +3x2 –5x +3x2 + 9x–15 = x3 + 6x2 +4x –15.
2). (xy–1) ( xy+5) = x2y2 + 5xy – xy –5 = x2y2 + 4xy – 5
3). (2x –5)(3x2 + 7x –1) = 2x(3x2 + 7x – 1) – 5( 3x2 + 7x – 1)
= 6x3 +14x2 – 2x – 15x2 – 35x+5 = 6x3 – x2 – 37x + 5.
4). (
xy –1)(x3 –2x –6) =
x4 y –x2y –3xy –x3 +2x + 6.
Áp dụng: (x – y) (x2 + xy + y2) = x (x2 + xy + y2) – y (x2 + xy + y2)
= x3 + x2y + xy2 – x2y – xy2 – y3 = x3 – y3

§ 3 . NHỮNG HẰNG ĐẲNG THỨC ĐÁNG NHỚ

1) (A + B)2 = A2 + 2AB + B2
2) (A – B)2 = A2 – 2AB + B2
3) A2 – B2 = (A + B)(A – B)
4) (A + B)3= A3+ 3A2B + 3AB2 + B3
5) (A – B)3= A3– 3A2B + 3AB2 – B3
6) A3 + B3 = (A + B)(A2– AB + B2)
7) A3 – B3 = (A – B)(A2 + AB + B2)











Bài 1. Nhân đơn thức với đa thức:
1). 3x2(5x2 – 2x – 4) 2). xy2(x2y + x3y2 + 3x2y3) 3). xyz(x2y + 3yz2 + 4xy2z)
4). 2x2(4x2 − 5xy + 8y3) 5). 2xy2(5x2 + 3xy − 6y3) 6). – x2y(xy2 –
xy +
x2y2)
7). (3xy – x2 + y).
x2y 8). (4x3 – 5xy + 2x)( –
xy) 9). 2x2(x2 + 3x +
)
10). –
x4y2(6x4 −
x2y3 – y5) 11).
x3(x + x2 –
x5) 12). 2xy2(xy + 3x2y –
xy3)
13). 3x(2x3 –
x2 – 4x) 14).
x3y5(7x4 + 5x2y −
x4y3 –y4)
Bài 2. Nhân đa thức với đa thức:
1). (2x ( 5)(3x + 7) 2). ((3x + 2)(4x ( 5) 3). (x ( 2)(x2 + 3x ( 1)
4).(x + 3)(2x2 + x ( 2) 5). (2x ( y)(4x2 ( 2xy + y2) 6). (x +3)(x2 –3x + 9) – (54 + x3)
7).(3x + 4x2 ( 2)(( x2 +1 + 2x) 8). (2x – y)(4x2 + 2xy + y2) 9). (2x + y)(4x2 – 2xy + y2)
10).(x – 2)(3x2 – 2x + 1) 11).(x + 2)(x2 + 3x + 2) 12.) (2x2 + 1)(x2 – x +3)
13).(xy – 1)(x2y – 3xy2) 14). (x + 3)(x2 – x + 2) 15). (x2 – x + 2)(2x – 3)
16).(x2 – 2xy – y2)(x