Bài giảng Đại số 7 - §6: Plus, except mode (Cộng, trừ đa thức)

Nội dung text: Bài giảng Đại số 7 - §6: Plus, except mode (Cộng, trừ đa thức)

1. CHECK OLDEST 1. Please remove parentheses in the following two expressions : a/ ( 5x2 – 3y + 2) + ( 4y – 2x2 – 2 ) b/ ( 5x2 – 3y + 2) – ( 4y – 2x2 – 2 ) 2. Please reduce the following polynomial: 5x2 – 3y + 2 + 4y – 2x2 – 2 3. Please reduce the following polynomial: 5x2 – 3y + 2 – 4y + 2x2 + 2
2. For two polynomials: A = 5x2 – 3y + 2 và B = 4y – 2x2 – 2 A + B = ( 5x2 – 3y + 2) + ( 4y – 2x2 – 2 ) A – B = ( 5x2 – 3y + 2) – ( 4y – 2x2 – 2 )
3. §6. PLUS, EXCEPT MODE 1. Add two polynomials +Ex: Add two polynomials : A = 5x2 – 3y + 2 và B = 4y – 2x2 – 2 A+ B =(5 x22 − 3 y + 2) +( 4 y − 2 x − 2) =5x22 − 3 y + 2 + 4 y − 2 x − 2 (remove brackets) = 5x22 + − 2 x + ( − 3 y) + 4 y + 2 +( − 2) (Apply commutative and ( ) coherent properties) 2 =+3xy(Add and subtract the same monomers) 2 We say: polynomial 3xy+ is the sum of two polynomials A and B
4. §6. PLUS, EXCEPT MODE 1. Add two polynomials 23 3 +EX 2: For : M= 3 x y − 4 y z + 2 và N= −5 y32 z + 8 x y − 2 x − 4 Calculation : M + N 2 3 3 2 3 MN+ =(3 xyyz − 4 + 2) + − 5 yzxyx + 8 − 2 − 4 3 =3x2 y − 4 y 3 z + 2 − 5 y 3 z + 8 x 2 y − 2 x − 4 2 2 3 3 −3 =(3x y + 8 x y) + ( − 4 y z) +( − 5 y z) + 2 + +( − 2 x) 4 5 =11x23 y +( − 9 y z) + +( − 2 x) 4 5 =11x23 y − 9 y z + − 2 x 4
5. Give two polynomials : A = 5x2 – 3y + 2 và B = 4y – 2x2 – 2 A – B = ( 5x2 – 3y + 2) – ( 4y – 2x2 – 2 )
6. . §6. PLUS, EXCEPT MODE 2. Subtract two polynomials +Ex1 Subtract two polynomials: A = 5x2 – 3y + 2 ,B = 4y – 2x2 – 2 A− B =(5 x22 − 3 y + 2) −( 4 y − 2 x − 2) =5x22 − 3 y + 2 − 4 y + 2 x + 2 (remove brackets) 22 =(5x + 2 x) + ( − 3 y) +( − 4 y) +( 2 + 2) (Applying commutative and associative properties) =7xy2 − 7 + 4 (Plus minus identical forms) We say: polynomial 7xy2 −+ 7 4 is the effect of two polynomials A and B
7. §6. PLUS, EXCEPT MODE 2. Subtract two polynomials 23 3 +Ex2: For: M= 3 x y − 4 y z + 2 andN = −5 y32 z + 8 x y − 2 x − 4 Calculation : M - N 2 3 3 2 3 MN− =(3 xyyz − 4 + 2) − − 5 yzxyx + 8 − 2 − 4 3 =3x2 y − 4 y 3 z + 2 + 5 y 3 z − 8 x 2 y + 2 x + 4 2 2 3 3 3 =3x y +( − 8 x y) +( − 4 y z) + 5 y z + 2 + + 2 x 4 11 = −52x23 y + y z + + x 4
8. Rule of addition (subtraction) of polynomial. Want to add or subtract polynomials we do the following: Step 1: Set properties. Step 2: Remove brackets. Step 3: Collapse the polynomial.
9. GROUP ACTIVITIES Give two polynomials : M=3 xyz − 3 x2 + 5 xy − 1 N=5 x2 + xyz − 5 xy + 3 − y Calculated: a/ M+N b/ M-N Group 1.2 makes sentences a. Group 3.4 makes sentences b.
10. Exercise 31 Textbook : Give two polynomials : M = 3xyz – 3x2 + 5xy – 1 và N = 5x2 + xyz – 5xy + 3 – y a) Calculation M + N Giải: M + N = (3xyz – 3x2 + 5xy –1) + (5x2 + xyz – 5xy + 3 – y) = 3xyz – 3x2 + 5xy –1 + 5x2 + xyz – 5xy + 3 – y = (3xyz + xyz)+(– 3x2 + 5x2)+(5xy – 5xy) – y + (–1 + 3) = 4xyz + 2x2 – y + 2
11. Exercise 31 Textbook : Give two polynomials : M = 3xyz – 3x2 + 5xy – 1 và N = 5x2 + xyz – 5xy + 3 – y b) Calculation M – N Solution : M – N = (3xyz – 3x2 + 5xy –1) – (5x2 + xyz – 5xy + 3 –y) = 3xyz – 3x2 + 5xy –1 – 5x2 – xyz + 5xy – 3 + y = (3xyz – xyz)+(– 3x2 – 5x2)+(5xy + 5xy) + y + (–1 – 3) = 2xyz – 8x2 + 10xy + y – 4
12. Exercise 32/40 Textbook Find P polynomials know : P+ (x2 − 2y 2 ) = x 2 − y 2 + 3y 2 − 1 Guide a) P+ (x2 − 2y 2 ) = x 2 − y 2 + 3y 2 − 1 P = (x2 − y 2 + 3y 2 − 1) − (x 2 − 2y 2 ) =x2 − y 2 +3 y 2 − 1 − x 2 + 2 y 2 =(x2 − x 2) +( − y 2 +3 y 2 + 2 y 2 ) − 1 =−41y2
13. Calculate the value of the following polynomial: A= x2 +2 xy − 3 x 3 + 2 y 3 + 3 x 3 − y 3 At x = 5 and y = 4 Giải A= x2 +2 xy − 3 x 3 + 2 y 3 + 3 x 3 − y 3 =( −3x3 + 3 x 3) +( 2 y 3 − y 3) + x 2 + 2 xy =y32 + x + 2 xy Replace x = 5 and y = 4 in the reduced polynomial, we get: 432++ 5 2.5.4 =64 + 25 + 40 =129 So the value of the above expression at x = 5 and y = 4 is 129
14. Cho hai đa thức: M=3 xyz − 3 x2 + 5 xy − 1 N=5 x2 + xyz − 5 xy + 3 − y Tính : a/ M+ N =(3 xyz − 3 x22 + 5 xy − 1) +( 5 x + xyz − 5 xy + 3 − y) 22 = 5x +−( 3 x) +( 3 xyz + xyz) + 5 xy +−( 5 xy) +−+−( 1 3) y =2x2 + 4 xyz + 2 − y
15. Cho hai đa thức: M=3 xyz − 3 x2 + 5 xy − 1 N=5 x2 + xyz − 5 xy + 3 − y Tính : b/ M− N =(3 xyz − 3 x22 + 5 xy − 1) −( 5 x + xyz − 5 xy + 3 − y) =3xyz − 3 x22 + 5 xy − 1 − 5 x − xyz + 5 xy − 3 + y 22 =− ( 5x) +−( 3 x) + 3 xyz +−( 1 xyz) +( 5 xy + 5 xy) +−+−+ ( 1) ( 3) y = −8x2 + 2 xyz + 10 xy − 4 + y