Các bài Luyện tập

Tiết 14
Luyện tập
Bài 54a/25
Phân tích đa thức sau thành nhân tử
x3 + 2x2y + xy2 – 9x
= x(x2 + 2xy + y2 – 9)
= x[(x + y)2 – 32]
= x(x + y + 3)(x + y – 3)
x3 + 2x2y + xy2 – 9x
= x(x2 + 2xy + y2 – 9)
= x[(x + y)2 – 32]
= x(x + y + 3)(x + y – 3)
x3 + 2x2y + xy2 – 9x
= x(x2 + 2xy + y2 – 9)
= x[(x + y)2 – 32]
= x(x + y + 3)(x + y – 3)
x3 + 2x2y + xy2 – 9x
= x(x2 + 2xy + y2 – 9)
= x[(x + y)2 – 32]
= x(x + y + 3)(x + y – 3)
x3 + 2x2y + xy2 – 9x
= x(x2 + 2xy + y2 – 9)
= x[(x + y)2 – 32]
= x(x + y + 3)(x + y – 3)
( A + B)
( A - B)
Bài 54b/25
Phân tích đa thức sau thành nhân tử
2x – 2y – x2 + 2xy – y2
= (2x – 2y) – (x2 – 2xy + y2)
= 2(x – y) – (x – y)2
= (x – y)(2 + x – y)(2 – x + y)
2x – 2y – x2 + 2xy – y2
= (2x – 2y) – (x2 – 2xy + y2)
= 2(x – y) – (x – y)2
= (x – y)(2 + x – y)(2 – x + y)
2x – 2y – x2 + 2xy – y2
= (2x – 2y) – (x2 – 2xy + y2)
= 2(x – y) – (x – y)2
= (x – y)(2 + x – y)(2 – x + y)
2x – 2y – x2 + 2xy – y2
= (2x – 2y) – (x2 – 2xy + y2)
= 2(x – y) – (x – y)2
= (x – y)(2 + x – y)(2 – x + y)
2x – 2y – x2 + 2xy – y2
= (2x – 2y) – (x2 – 2xy + y2)
= 2(x – y) – (x – y)2
= (x – y)(2 + x – y)(2 – x + y)
2x – 2y – x2 + 2xy – y2
= (2x – 2y) – (x2 – 2xy + y2)
= 2(x – y) – (x – y)2
= (x – y)(2 – x + y)
2x – 2y – x2 + 2xy – y2
= (2x – 2y) – (x2 – 2xy + y2)
= 2(x – y) – (x – y)2
= (x – y)(2 – x + y)
Bài 55b/25
Phân tích đa thức sau thành nhân tử
(2x – 1)2 – (x + 3)2
= [(2x – 1) + (x + 3)][(2x – 1) – (x + 3)]
= (2x – 1 + x + 3)(2x – 1 – x – 3)
(2x – 1)2 – (x + 3)2
= [(2x – 1) + (x + 3)][(2x – 1) – (x + 3)]
= (2x – 1 + x + 3)(2x – 1 – x – 3)
(2x – 1)2 – (x + 3)2
= [(2x – 1) + (x + 3)][(2x – 1) – (x + 3)]
= (2x – 1 + x + 3)(2x – 1 – x – 3)
(2x – 1)2 – (x + 3)2
= [(2x – 1) + (x + 3)][(2x – 1) – (x + 3)]
= (2x – 1 + x + 3)(2x – 1 – x – 3)
= (3x + 2)(x – 4)
Bài 55c/25
Phân tích đa thức sau thành nhân tử
x2(x – 3) + 12 – 4x
= x2(x – 3) – 4(x – 3)
= (x – 3)(x2 – 4)
= (x – 3)(x + 2)(x – 2)
x2(x – 3) + 12 – 4x
= x2(x – 3) – 4(x – 3)
= (x – 3)(x2 – 4)
= (x – 3)(x + 2)(x – 2)
x2(x – 3) + 12 – 4x
= x2(x – 3) – 4(x – 3)
= (x – 3)(x2 – 4)
= (x – 3)(x + 2)(x – 2)
x2(x – 3) + 12 – 4x
= x2(x – 3) – 4(x – 3)
= (x – 3)(x2 – 4)
= (x – 3)(x + 2)(x – 2)
Bài 56b/25
Tính giá trị đa thức
x2 – y2 – 2y – 1 tại x = 93 và y = 6
Giải
x2 – y2 – 2y – 1
= x2 – (y2 + 2y + 1)
= x2 – (y + 1)2
= (x + y + 1)(x – y – 1)
= (93+6+1)(93–6–1) (x=93 và y=6)
= 100.86 = 8600
x2 – y2 – 2y – 1
= x2 – (y2 + 2y + 1)
= x2 – (y + 1)2
= (x + y + 1)(x – y – 1)
= (93+6+1)(93–6–1) (x=93 và y=6)
= 100.86 = 8600
x2 – y2 – 2y – 1
= x2 – (y2 + 2y + 1)
= x2 – (y + 1)2
= (x + y + 1)(x – y – 1)
= (93+6+1)(93–6–1) (x=93 và y=6)
= 100.86 = 8600
x2 – y2 – 2y – 1
= x2 – (y2 + 2y + 1)
= x2 – (y + 1)2
= (x + y + 1)(x – y – 1)
= (93+6+1)(93–6–1) (x=93 và y=6)
= 100.86 = 8600
x2 – y2 – 2y – 1
= x2 – (y2 + 2y + 1)
= x2 – (y + 1)2
= (x + y + 1)(x – y – 1)
= (93+6+1)(93–6–1) (x=93 và y=6)
= 100.86 = 8600
Bài 57a/25
Phân tích đa thức sau thành nhân tử
x2 – 4x + 3
= x2 – x – 3x + 3
= (x2 – x) – (3x – 3)
= x(x – 1) – 3(x – 1)
= (x – 1)(x – 3)
x2 – 4x + 3
= x2 – x – 3x + 3
= (x2 – x) – (3x – 3)
= x(x – 1) – 3(x – 1)
= (x – 1)(x – 3)
x2 – 4x + 3
= x2 – x – 3x + 3
= (x2 – x) – (3x – 3)
= x(x – 1) – 3(x – 1)
= (x – 1)(x – 3)
x2 – 4x + 3
= x2 – x – 3x + 3
= (x2 – x) – (3x – 3)
= x(x – 1) – 3(x – 1)
= (x – 1)(x – 3)
x2 – 4x + 3
= x2 – x – 3x + 3
= (x2 – x) – (3x – 3)
= x(x – 1) – 3(x – 1)
= (x – 1)(x – 3)
BÀI TẬP
Phân tích các đa thức sau đây thành nhân tử
Bài 47a/ 22
x2 – xy + x – y
=(x2 – xy) + (x – y)
=x(x – y) + (x – y)
=(x – y)(x + 1)
x2 – xy + x – y
=(x2 – xy) + (x – y)
=x(x – y) + (x – y)
=(x – y)(x + 1)
x2 – xy + x – y
=(x2 – xy) + (x – y)
=x(x – y) + (x – y)
=(x – y)(x + 1)
x2 – xy + x – y
=(x2 – xy) + (x – y)
=x(x – y) + (x – y)
=(x – y)(x + 1)
x2 – xy + x – y
=(x2 – xy) + (x – y)
=x(x – y) + (x – y)
=(x – y)(x + 1)
x2 – xy + x – y
=(x2 – xy) + (x – y)
=x(x – y) + (x – y)
=(x – y)(x + 1)
x2 – xy + x – y
=(x2 – xy) + (x – y)
=x(x – y) + (x – y)
=(x – y)(x + 1)
x2 – xy + x – y
=(x2 – xy) + (x – y)
=x(x – y) + (x – y)
=(x – y)(x + 1)
x2 – xy + x – y
=(x2 – xy) + (x – y)
=x(x – y) + (x – y)
=(x – y)(x + 1)
Nhóm cách 2
Phân tích các đa thức sau đây thành nhân tử
Bài 47c/ 22
3x2 – 3xy – 5x + 5y
=(3x2 – 3xy) – (5x – 5y)
=3x(x – y) -5(x – y)
= (x – y)(3x – 5)
3x2 – 3xy – 5x + 5y
=(3x2 – 3xy) – (5x – 5y)
=3x(x – y) -5(x – y)
= (x – y)(3x – 5)
3x2 – 3xy – 5x + 5y
=(3x2 – 3xy) – (5x – 5y)
=3x(x – y) -5(x – y)
= (x – y)(3x – 5)
3x2 – 3xy – 5x + 5y
=(3x2 – 3xy) – (5x – 5y)
=3x(x – y) -5(x – y)
= (x – y)(3x – 5)
3x2 – 3xy – 5x + 5y
=(3x2 – 3xy) – (5x – 5y)
=3x(x – y) -5(x – y)
= (x – y)(3x – 5)
3x2 – 3xy – 5x + 5y
=(3x2 – 3xy) – (5x – 5y)
=3x(x – y) -5(x – y)
= (x – y)(3x – 5)
3x2 – 3xy – 5x + 5y
=(3x2 – 3xy) – (5x – 5y)
=3x(x – y) -5(x – y)
= (x – y)(3x – 5)
Phân tích các đa thức sau đây thành nhân tử
Bài 48a/ 22
x2 + 4x – y2 + 4
= x2 + 4x + 4 – y2
= (x2 + 4x + 4) – y2
= (x + 2)2 – y2
= (x + 2 + y)(x + 2 – y)
x2 + 4x – y2 + 4
= x2 + 4x + 4 – y2
= (x2 + 4x + 4) – y2
= (x + 2)2 – y2
= (x + 2 + y)(x + 2 – y)
3 số hạng này lập thành hằng đẳng thức gì?
Tìm cách nhóm thích hợp
x2 + 4x – y2 + 4
= x2 + 4x + 4 – y2
= (x2 + 4x + 4) – y2
= (x + 2)2 – y2
= (x + 2 + y)(x + 2 – y)
x2 + 4x – y2 + 4
= x2 + 4x + 4 – y2
= (x2 + 4x + 4) – y2
= (x + 2)2 – y2
= (x + 2 + y)(x + 2 – y)
x2 + 4x – y2 + 4
= x2 + 4x + 4 – y2
= (x2 + 4x + 4) – y2
= (x + 2)2 – y2
= (x + 2 + y)(x + 2 – y)
x2 + 4x – y2 + 4
= x2 + 4x + 4 – y2
= (x2 + 4x + 4) – y2
= (x + 2)2 – y2
= (x + 2 + y)(x + 2 – y)
Phân tích các đa thức sau đây thành nhân tử
Bài 48b/ 22
3x2 + 6xy + 3y2 – 3z2
= 3(x2 + 2xy + y2 – z2)
= 3[(x + y)2 – z2]
= 3(x + y + z)(x + y – z)
3x2 + 6xy + 3y2 – 3z2
= 3(x2 + 2xy + y2 – z2)
= 3[(x + y)2 – z2]
= 3(x + y + z)(x + y – z)
3x2 + 6xy + 3y2 – 3z2
= 3(x2 + 2xy + y2 – z2)
= 3[(x + y)2 – z2]
= 3(x + y + z)(x + y – z)
3x2 + 6xy + 3y2 – 3z2
= 3(x2 + 2xy + y2 – z2)
= 3[(x + y)2 – z2]
= 3(x + y + z)(x + y – z)
3x2 + 6xy + 3y2 – 3z2
= 3(x2 + 2xy + y2 – z2)
= 3[(x + y)2 – z2]
= 3(x + y + z)(x + y – z)
DẶN DÒ
Làm các bài tập 54c, 55a, 57bc/25