Bài toán 1 : Tính
1. (x + 2y)2 11. (x/2 - 2y)
2 . (2x + 3y)2 12. (Căn 2x - y)2
3. (3x - 2y)2 13. (3/2x + 3y)2
4. (5x - y)2 14. (Căn 2x + căn 8y)2
5. (x + 1/4)2 15. (x + 1/6y + 3)2
6. (2x - 1/2)2 16. (1/2x - 4y)2
7. (1/3x - 1/2y)2 17. (x/2 + 2y2) (x/2 - 2y2)
8. (3x + 1) (3x - 1) 18. (x2 - 4) (x2 + 4)
9. (x2 + 2/5y) (x2 - 2/5y) 19. (x + y)2 + (x - y)2
10. (x/2 - y) (x/2 + y) 20. (2x + 3)2 - (x + 1)2
Bài toán 2 : Viết các đa thức sau thành tích
1. x2 - 6x + 9 1. (3x + 2)2 - 4
2. 25 + 10x + x2 2. 4x2 - 25y2
3. 1/4a2 + 2ab2 + 4b4 3. 4x2 - 49
4. 1/9 - 2/3y4 + y8 5. 9/25x4 - 1/4
5. x2 - 10x + 25 6. x32 - 1
6. x2 + 4xy + 4y2 7. 4x2 + 4x + 1
8. x2 - 20x + 100
9. y4 - 14y2 + 49
Bài toán 3 : Tính nhanh
1. 10012 6. 372 + 2 . 37 . 13 + 132
2. 29,9 . 30,1 7. 51,7 - 2 . 51,7 . 31,7 + 31,72
3. 2012 8. 20,1 . 19,9
4. 37 . 43 9. 31,82 - 2 . 31,8 . 21,8 + 21,82
5. 1992 10. 33,32 - 2 . 33,3 . 3,3 + 3,32
Bài toán 4 : Rút gọn rồi tính giá trị biểu thức
1. (x - 10)2 - x(x + 80) với x = 0,98 5. 9x2 + 42x + 49 với x = 1
2. (2x + 9)2 - x(4x + 31) với x = -16,2 6. 25x2 - 2xy + 1/25y2 với x = -1/5 , y = - 5
3. 4x2 - 28x + 49 với x = 4
Bài toán 5 : Viết mỗi biểu thức sau dưới dạng tổng hoặc hiệu hiệu hai bình phương
1. x2 + 10x + 26 + y2 + 2y 6. 4x2 + 2z2 - 4zx - 2z + 1
2. z2 - 6z + 13 + t2 + 4t 7. (x + y + 4) ( x + y - 4)
3. x2 - 2xy + 2y2 + 2y + 1 8. (x - y + 6) (x + y - 6)
4. 4x2 + 2z2 - 4xz - 2z + 1 9. (y + 2z - 3) ( y - 2z - 3)
5. 4x2 - 12x - y2 + 2y + 8 10. (x + 2y + 3z) (2y + 3z - x)
Dài rứa :v
Bài 1.
1. ( x + 2y )2 = x2 + 4xy + 4y2
2. ( 2x + 3y )2 = 4x2 + 12xy + 9y2
3. ( 3x - 2y )2 = 9x2 - 12xy + 4y2
4. ( 5x - y )2 = 25x2 - 20xy + y2
5. ( x + 1/4 )2 = x2 + 1/2x + 1/16
6. ( 2x - 1/2 )2 = 4x2 - 2x + 1/4
7. ( 1/3x - 1/2y )2 = 1/9x2 - 1/3xy + 1/4y2
8. ( 3x + 1 )( 3x - 1 ) = ( 3x )2 - 12 = 9x2 - 1
9. ( x2 + 2/5y )( x2 - 2/5y ) = ( x2 )2 - ( 2/5y )2 = x4 - 4/25y2
10. ( x/2 + y )( x/2 - y ) = ( x/2 )2 - y2 = x2/4 - y2
11. Chưa rõ đề
12. \(\left(\sqrt{2x}-y\right)^2=2x-2\sqrt{2x}\cdot y+y^2\)
13. ( 3/2x + 3y )2 = 9/4x2 + 9xy + 9y2
14. \(\left(\sqrt{2x}+\sqrt{8y}\right)^2=2x+\left(2\sqrt{2x}\sqrt{8y}\right)+8y\)
15. ( x + 1/6y + 3 )2 = [( x + 1/6y ) + 3 ]2 = x2 + 1/3xy + 1/36y2 + 6x + y + 9
16. ( 1/2x - 4y )2 = 1/4x2 - 4xy + 16y2
17. ( x/2 + 2y2 )( x/2 - 2y2 ) = ( x/2 )2 - ( 2y2 )2 = x2/4 - 4y4
18. ( x2 - 4 )( x2 + 4 ) = ( x2 )2 - 42 = x4 - 16
19. ( x + y )2 + ( x - y )2 = x2 + 2xy + y2 + x2 - 2xy - y2 = 2x2 + 2y2 = 2( x2 + y2 )
20. ( 2x + 3 )2 - ( x + 1 )2 = [ 2x + 3 + x + 1 ][ 2x + 3 - ( x + 1 )] = [ 3x + 4 ][ x + 2 ]
1. (x + 2y)2 = (x + 2y)(x + 2y) = x(x + 2y) + 2y(x + 2y) = x2 + 2xy + 2xy + 4y2 = x2 + 4xy + 4y2
2. (2x + 3y)2 = (2x + 3y)(2x + 3y) = 2x(2x + 3y) + 3y(2x + 3y) = 4x2 + 6xy + 6xy + 9y2 = 4x2 + 12xy + 9y2
3. (3x - 2y)2 = (3x - 2y)(3x - 2y) = 3x(3x - 2y) - 2y(3x - 2y) = 9x2 - 6xy - 6xy + 4y2 = 9x2 - 12xy + 4y2
4. (5x - y)2 = (5x - y)(5x - y) = 5x(5x - y) - y(5x - y) = 25x2 - 5xy - 5xy - y2 = 25x2 - 10xy - y2
5. (x + 1/4)2 = (x + 1/4)(x + 1/4)
= x(x + 1/4) + 1/4(x + 1/4)
= x2 + 1/4x + 1/4x + 1/16
= x2 + 1/2x + 1/16
6. (2x - 1/2)2 = (2x - 1/2)(2x - 1/2)
= 2x(2x - 1/2) - 1/2(2x - 1/2)
= 4x2 - x - x + 1/4
= 4x2 - 2x + 1/4
7. (1/3x - 1/2y)2 = (1/3x - 1/2y)(1/3x - 1/2y)
= 1/3x(1/3x - 1/2y) - 1/2y(1/3x - 1/2y)
= 1/9x2 - 1/6xy - 1/6xy + 1/4y2
= 1/9x2 - 1/3xy + 1/4y2
8. (3x + 1)(3x - 1)
= 3x(3x - 1) + 1(3x - 1)
= 9x2 - 3x + 3x - 1
= 9x2 - 1
9. \(\left(x^2+\frac{2}{5}y\right)\left(x^2-\frac{2}{5}y\right)\)
= x2(x2 - 2/5y) + 2/5y(x2 - 2/5y)
= x4 - 2/5x2y + 2/5x2y - 4/25y2
= x4 - 4/25y2
10. \(\left(\frac{x}{2}-y\right)\left(\frac{x}{2}+y\right)\)
= \(\frac{x}{2}\left(\frac{x}{2}+y\right)-y\left(\frac{x}{2}+y\right)\)
= \(\frac{x^2+2xy}{4}-\frac{2y^2+xy}{2}\)
= \(\frac{x^2+2xy}{4}-\frac{2\left(2y^2+xy\right)}{4}=\frac{x^2+2xy-4y^2-2xy}{4}\)
= \(\frac{x^2-4y^2}{4}\)
11. Giữ nguyên
Làm nốt đi nhé chứ mỏi tay lắm rồi
Bài 4 : \(\left(x-10\right)^2-x\left(x+80\right)\)
= (x - 10)(x - 10) - x2 - 80x
= x(x- 10) - 10(x - 10) - x2 - 80x
= x2 - 10x - 10x + 100 - x2 - 80x
= (x2 - x2) + (-10x - 10x - 80x) + 100
= -100x + 100 = -100(x - 1)
Thay x = 0,98 vào biểu thức trên ta có :
-100(x - 1) = -100(0,98 - 1) = -100.(-0,02) = 2
2. (2x + 9)2 - x(4x + 31)
= (2x + 9)(2x + 9) - 4x2 - 31x
= 2x(2x + 9) + 9(2x + 9) - 4x2 - 31x
= 4x2 + 18x + 18x + 18 - 4x2 - 31x
= (4x2 - 4x2) + (18x + 18x - 31x) + 18
= 5x + 18
Thay x = -16,2 vào biểu thức trên ta có : 5.(-16,2) + 18 = -63
3. Thay x = 4 vào biểu thức trên ta có :
4.42 - 28.4 + 49 = 4.16 - 112 + 49 = 64 - 112 + 49 = 1
4. Thay x = 1 vào biểu thức trên ta có :
9.12 + 42.1 + 49 = 9 + 42 + 49 = 100
5. Thay x = -1/5 ; y = -5 vào biểu thức trên ta có :
25. (-1/5)2 - 2.(-1/5) . (-5) + 1/25 . (-5)2
= 25 . 1/25 - 2 + 1
= 1 - 2 + 1 = 0
Lần sau đăng ít bài thôi
Bài 5.
1. x2 + 10x + 26 + y2 + 2y = ( x2 + 10x + 25 ) + ( y2 + 2y + 1 ) = ( x + 5 )2 + ( y + 1 )2
2. z2 - 6z + 13 + t2 + 4t = ( z2 - 6z + 9 ) + ( t2 + 4t + 4 ) = ( z - 3 )2 + ( t + 2 )2
3. x2 - 2xy + 2y2 + 2y + 1 = ( x2 - 2xy + y2 )+ ( y2 + 2y + 1 ) = ( x - y )2 + ( y + 1 )2
4. 4x2 + 2z2 - 4xz - 2z + 1 = ( 4x2 - 4xz + z2 ) + ( z2 - 2z + 1 ) = ( 2x - z )2 + ( z - 1 )2
5. 4x2 - 12x - y2 + 2y + 8 = ( 4x2 - 12x + 9 ) - ( y2 - 2y + 1 ) = ( 2x - 3 )2 - ( y - 1 )2
6. 4x2 + 2z2 - 4zx - 2z + 1 = ( 4x2 - 4xz + z2 ) + ( z2 - 2z + 1 ) = ( 2x - z )2 + ( z - 1 )2
7. ( x + y + 4 )( x + y - 4 ) = [ ( x + y ) + 4 ][ ( x + y ) - 4 ] = ( x + y )2 - 42
8. ( x - y + 6 )( x + y - 6 ) = [ x - ( y + 6 ) ][ x + ( y - 6 ) ] = x2 - ( y + 6 )2
9. ( y + 2z - 3 )( y - 2z + 3 ) = [ y + ( 2z - 3 )][ y - ( 2z - 3 )] = y2 - ( 2z - 3 )2
10. ( x + 2y + 3z )( 2y + 3z - x ) = ( 2y + 3z )2 - x2
