Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a) x2 - 2x - 4y2 - 4y
= (x2 - 4y2) - (2x + 4y)
= (x + 2y)(x - 2y) - 2(x + 2y)
= (x + 2y)(x - 2y - 2)
= (x + 2y)[x - 2(y + 1)]
b) x4 + 2x3 - 4x - 4
= (x4 - 4) + ( 2x3 - 4x)
= (x2 - 2)(x2 + 2) + 2x(x2 - 2)
= (x2 - 2)(x2 + 2 + 2x)
c) x3 + 2x2y - x -2y
= (x3 - x) + (2x2y - 2y)
= x(x2 - 1) + 2y(x2 - 1)
= (x + 2y)(x2 - 1)
\(1.5x\left(x^2+2x-1\right)-3x^2\left(x-2\right)=5x^3+10x^2-5x-3x^3+6x^2\)
\(=2x^3+16x^2-5x\)
\(=\left(2x^3-x\right)+\left(16x^2-4x\right)\)
\(=x\left(2x^2-1\right)+4x\left(4x-1\right)\left(ĐCCM\right)\)
a, \(x^2\) + 6x + 5 = 0
=>\(x^2\) + x + 5x +5 = 0
=>x(x + 1) + 5(x + 1) = 0
=>(x + 1)(x + 5) = 0
=> x + 1 =0 hoặc x + 5 =0
=> x = -1 hoặc x = -5
a ) \(x^2-x+1\)
\(\Leftrightarrow\left(x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2\right)+\dfrac{3}{4}\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\)
Ta có : \(\left(x-\dfrac{1}{2}\right)^2\ge0\forall x\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\)
Vậy GTNN là \(\dfrac{3}{4}\Leftrightarrow x=\dfrac{1}{2}.\)
a) 2x2.(5x3-4x2y-7xy +1) =10x5-8x4y-14x3y+2x2 b) (5x -2y)(x2 -xy +1) =5x3-5x2y+5x-2x2y+2xy2-2y =5x3-7x2y+2xy2+5x-2y c) (\(\dfrac{1}{2}\)x -1)(2x -3) =x2-\(\dfrac{3}{2}\)x-2x+3 =x2-\(\dfrac{7}{2}\)x+3 d) (x +3y)2 =x2+6xy+9y2 e) (3x -2y)2 =9x2-12xy+4y2 g) (\(\dfrac{1}{4}\)x - 3y)(\(\dfrac{1}{4}\)x +3y) =\(\dfrac{1}{16}\)x2-9y2 f) (2x +3)3 =8x3+36x2+54x+27 h) (3 -2y)3 =27-54y+36y2-8y3
1,4x2.(5x3+2x-1)
=4x2.5x3+4x2.2x-4x2.1
20x5+8x3-4x2
2,4x3y2:x2
=4xy2
3,(15x2y3-10x3y3+6xy):5xy
15x2y3:5xy-10x3y3:5xy+6xy:5xy
3xy2-2x2y2+\(\dfrac{6}{5}\)
1: \(=20x^5+8x^3-4x^2\)
2: \(=4xy^2\)
3: \(=3xy^2-2x^2y^2+\dfrac{6}{5}\)
4: \(=\dfrac{5x^3+10x^2+4x^2+8x+4x+8}{x+2}=5x^2+4x+4\)
5: \(=\dfrac{7}{2x}+\dfrac{11}{3y^2}=\dfrac{21y^2+22x}{6xy^2}\)
6: \(=\dfrac{4x^2-7x+3}{\left(4x-7\right)\left(x+2\right)}\)
7: \(=\dfrac{3x+3y-2x^3+2x^2y}{\left(x-y\right)\left(x+y\right)}\)
8: \(=\dfrac{1}{2}x^2y^2\left(4x^2-y^2\right)=2x^4y^2-\dfrac{1}{2}x^2y^4\)
9: \(=\left(x-\dfrac{1}{4}\right)\left(4x-1\right)=4\left(x-\dfrac{1}{4}\right)^2=4\left(x^2-\dfrac{1}{2}x+\dfrac{1}{16}\right)\)
\(=4x^2-2x+\dfrac{1}{4}\)
10: \(=\dfrac{3x^2+6-x}{x\left(2x+6\right)}=\dfrac{2x+6}{x\left(2x+6\right)}=\dfrac{1}{x}\)
11: \(=\dfrac{x+1}{2}-\dfrac{3}{x-1}\)
\(=\dfrac{x^2-7}{2\left(x-1\right)}\)
12: \(=\dfrac{x^2-xy}{\left(x-y\right)\left(x+y\right)}=\dfrac{x}{x+y}\)
15:=x^3-y^3+2
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