Toán Lớp 8: Bài 1: Rút gọn các biểu thức sau:
a.(x – 3)(x + 7) – (x + 5)(x -1) b. (x + 8)2 – 2(x +8)(x -2) + (x -2)2
c. x2(x – 4)(x + 4) – (x2 + 1)(x2- 1) d. (x+1)(x2 – x + 1) – (x – 1)(x2 +x +1)
Bài 2: Phân tích các đa thức sau thành nhân tử:
a. x2 – 6 x + xy – 6y b. 2×2 + 2xy – x – y c. x2 – 2xy – x2 + 4y2
d. x2 + 2x + 1 – 16 e. x2 + x – 6 f. x2 -5x -6
g, x2 + 6x +8 h*. x7 + x2 + 1
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Comments ( 1 )
a/ (x – 3)(x + 7) – (x + 5)(x -1)
= x²+7x-3x-21-x²+x-5x+5
= (x²-x²)+(7x-3x+x-5x)+(-21+5)
= -16
b/ (x + 8)² – 2(x +8)(x -2) + (x -2)²
= (x+8-x+2)²=10²=100
c/ x²(x – 4)(x + 4) – (x² + 1)(x²- 1)
= x²(x²-16)-($x^{4}$ -1)
= x^4-16x²-x^4+1
= -16x²+1
d/ (x+1)(x² – x + 1) – (x – 1)(x² +x +1)
= x³+1-x³+1=2
2)
a. x²–6x+xy-6y
= x(x+y)-6(x+y)
= (x+y)(x-6)
b. 2x²+2xy-x-y
= x(2x-1)-y(2x-1)
= (2x-1)(x-y)
c. x² – 2xy – x² + 4y²
= -2xy+4y²
= 2y(y-x)
d. x² + 2x + 1 – 16
= (x+1)²-4²
= (x+1-4)(x+1+4)
= (x-3)(x+5)
e. x²+x-6
= x²+3x-2x-6
= x(x+3)-2(x+3)
= (x+3)(x-2)
f. x²-5x-6
= x²+x-6x-6
= x(x+1)-6(x+1)
= (x-6)(x+1)
g. x²+6x+8
= x²+2.3.x+9-1
= (x-3)²-1
= (x-3-1)(x-3+1)
= (x-4)(x-2)
h*. x^7+x²+1
= (x²+x+1)(x^5-x^4+x²-x+1)
(chúc bạn học tốt=3)