Bài giảng Đại số Lớp 8 - Tiết 14: Luyện tập

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