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5 tháng 7 2017

Cứ thay vào rùi thính thui

5 tháng 7 2017

Mấy bài kia phá tung tóe rồi rút gọn hết sức xong thay x vào, làm câu c thôi nhé:

c) \(C=x^{14}-10x^{13}+10x^{12}-10x^{11}+...+10x^2-10x+10\)

riêng câu này ta thay x = 9 vào luôn, vậy ta có:

\(C=9^{14}-10\cdot9^{13}+10\cdot9^{12}-10\cdot9^{11}+...+10\cdot9^2-10\cdot9+10\)

\(=9^{14}-\left(9+1\right)\cdot9^{13}+\left(9+1\right)\cdot9^{12}-\left(9+1\right)\cdot9^{11}+...+\left(9+1\right)\cdot9^2-\left(9+1\right)\cdot9+10\)

\(=9^{14}-9^{14}-9^{13}+9^{13}+9^{12}-9^{12}-9^{11}+...+9^3+9^2-9^2-9+10\)

\(=-9+10\)

\(=1\)

27 tháng 9 2020

a, x4 + 2x3 +x2 = x+x+x3 +x2  =(x4+x3 )+(x3 +x) =x3(x +1 ) + x(x+1 ) =(x+1)(x3+x2)

27 tháng 9 2020

a) x4 + 2x3 + x2

= x2(x2 + 2x + 1)

= x2(x + 1)2

= [x(x + 1)]2

= (x2 + x)2

b) 5x3 - 10xy + 5y2 - 20z2

= 5(x3 - 2xy + y2 - 4z2)

c) x2y - xy2 + x3 - y3

= xy(x - y) + (x - y)(x2 + xy + y2)

= (x - y)(x2 + 2xy + y2)

= (x - y)(x + y)2

d) x2 - xy + 4x - 2y  + 4

= (x2 + 4x + 4) - (xy + 2y)

= (x + 2)2 - y(x + 2)

= (x + 2)(x + 2 - y)

d) x2 - x - 6

= x2 - 3x + 2x - 6

= x(x - 3) + 2(x - 3)

= (x + 2)(x - 3)

f) 3x2 - 5x - 8

= 3x2 + 3x - 8x - 8

= 3x(x + 1) - 8(x + 1)

= (3x - 8)(x + 1)

g) x3 + 3x2 + 6x + 4

= (x3 + 3x2 + 3x + 1) + (3x + 3)

= (x + 1)3 + 3(x + 1)

= (x + 1)[(x + 1)2 + 3]

h) 3x3 - 5x2 - 6x + 8

= 3x3 - 3x2 - 2x2 - 6x + 8

= 3x3 - 3x2 - 2x2 + 2x - 8x + 8

= 3x2(x - 1) - 2x(x - 1) - 8(x - 1)

= (3x2 - 2x - 8)(x - 1)

27 tháng 9 2020

a) \(x^4+2x^3+x^2=x^2\left(x^2+2x+1\right)=x^2\left(x+1\right)^2\)

b) \(5x^2-10xy+5y^2-20z^2\) (đã sửa đề)

\(=5\left[\left(x^2-2xy+y^2\right)-4z^2\right]\)

\(=5\left[\left(x-y\right)^2-\left(2z\right)^2\right]\)

\(=5\left(x-y-2z\right)\left(x-y+2z\right)\)

c) \(x^2y-xy^2+x^3-y^3\)

\(=xy\left(x-y\right)+\left(x-y\right)\left(x^2+xy+y^2\right)\)

\(=\left(x-y\right)\left(x^2+2xy+y^2\right)\)

\(=\left(x-y\right)\left(x+y\right)^2\)

27 tháng 9 2020

d) \(x^2-xy+4x-2y+4\)

\(=\left(x^2+4x+4\right)-\left(xy+2y\right)\)

\(=\left(x+2\right)^2-y\left(x+2\right)\)

\(=\left(x+2\right)\left(x-y+2\right)\)

e) \(x^2-x-6=\left(x+2\right)\left(x-3\right)\)

f) \(3x^2-5x-8\)

\(=\left(3x^2+3x\right)-\left(8x+8\right)\)

\(=3x\left(x+1\right)-8\left(x+1\right)\)

\(=\left(x+1\right)\left(3x-8\right)\)

1 tháng 8 2018

\(a.x^2-y^2-5x+5y=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x-y\right)\left(x+y-5\right)\) \(b.5x^3-5x^2y-10x^2+10xy=5x^2\left(x-y\right)-10x\left(x-y\right)=5x\left(x-y\right)\left(x-2\right)\) \(c.x^3-2x^2-4xy^2+x=x\left(x^2-2x+1-4y^2\right)=x\left[\left(x-1\right)^2-4y^2\right]=\left(x-1-2y\right)\left(x-1+2y\right)\) \(d.\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-8=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-8\)

Đặt : \(x^2+7x+11=t\) , ta có :

\(\left(t+1\right)\left(t-1\right)-8=t^2-1-8=\left(t-3\right)\left(t+3\right)=\left(x^2+7x+8\right)\left(x^2+7x+14\right)\)

\(e.2x^2-5x-7=2x^2+2x-7x-7=2x\left(x+1\right)-7\left(x+1\right)=\left(x+1\right)\left(2x-7\right)\) \(f.x^2-12x+36=\left(x-6\right)^2=\left(x-6\right)\left(x-6\right)\)

\(g.x^4-5x^2+4=x^4-x^2-4x^2+4=x^2\left(x^2-1\right)-4\left(x^2-1\right)=\left(x^2-1\right)\left(x^2-4\right)=\left(x+1\right)\left(x-1\right)\left(x+2\right)\left(x-2\right)\) \(g.a^3+b^3+c^3-3abc=\left(a+b\right)^3+c^3-3ab\left(a+b\right)-3abc=\left(a+b+c\right)\left[\left(a+b\right)^2-c\left(a+b\right)+c^2\right]-3ab\left(a+b+c\right)=\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2-3ab\right)=\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ac\right)\)

10 tháng 10 2017

Câu a trước đi ạ ^^

a) 7x - 6x- 2

= - 6x2 + 7x - 2

= (- 6x2 + 3x) + (4x - 2)

= 3x (- 2x + 1) + 2 (2x-1)

= - 3x ( 2x -1) + 2 (2x - 1)

= ( 2x -1 ) ( - 3x +2 )

AH
Akai Haruma
Giáo viên
21 tháng 12 2018

a)

\(14x^2y-21xy^2+28x^2y^2\)

\(=7xy(2x-3y+4xy)\)

b) \(x(x+y)-5x-5y=x(x+y)-5(x+y)=(x-5)(x+y)\)

c)

\(10x(x-y)-8(y-x)=10x(x-y)+8(x-y)\)

\(=(x-y)(10x+8)=2(x-y)(5x+4)\)

21 tháng 12 2018

a. \(14x^2y-21xy^2+28x^2y^2\)

\(=7xy\left(2x-3y+4xy\right)\)

b. \(x\left(x+y\right)-5x-5y\)

\(=x\left(x+y\right)-5\left(x+y\right)\)

\(=\left(x-5\right)\left(x+y\right)\)

c. \(10x\left(x-y\right)-8\left(y-x\right)\)

\(=10x\left(x-y\right)+8\left(x-y\right)\)

\(=\left(10x+8\right)\left(x-y\right)\)

d. \(\left(3x+1\right)^2-\left(x+1\right)^2\)

\(=\left(3x+1+x+1\right)\left(3x+1-x-1\right)\)

\(=2x\left(4x+2\right)\)

\(=4x\left(2x+1\right)\)

e. Vì bài này giải không ra nên mình nghĩ nó sai đề, sửa lại tí nhé!

\(x^3+y^3+z^3-3xyz\)

\(=\left(x+y\right)^3+z^3-3xy\left(x+y\right)-3xyz\)

\(=\left(x+y+z\right)\left[\left(x+y\right)^2-z\left(x+y\right)+z^2\right]-3xy\left(x+y+z\right)\)

\(=\left(x+y+z\right)\left(x^2+2xy+y^2-xz+zy+z^2-3xy\right)\)

g. \(5x^2-10xy+5y^2-20z^2\)

\(=5\left(x^2-2xy+y^2-4z^2\right)\)

\(=5\left[\left(x-y^2\right)-4z^2\right]\)

\(=5\left(x-y+z\right)\left(x-y-z\right)\)

h. \(x^3-x+3x^2y+3xy^3+y^3-y\)

\(=\left(x^3+3x^2y+3xy^2+y^2\right)-\left(x+y\right)\)

\(=\left(x+y\right)^3-\left(x+y\right)\)

\(=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)

\(=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)

i. \(x^2+7x-8\)

\(=x^2-x+8x-8\)

\(=x\left(x-1\right)+8\left(x-1\right)\)

\(=\left(x+8\right)\left(x-1\right)\)

22 tháng 9 2020

a) x2 + x - 12 = x2 - 3x + 4x - 12 = x( x - 3 ) + 4( x - 3 ) = ( x - 3 )( x + 4 )

b) x2 - 4x - 5 = x2 + x - 5x - 5 = x( x + 1 ) - 5( x + 1 ) = ( x + 1 )( x - 5 )

c) x2 - 2x - 3 = x2 + x - 3x - 3 = x( x + 1 ) - 3( x + 1 ) = ( x + 1 )( x - 3 )

d) x2 - 2x - 8 = x2 + 2x - 4x - 8 = x( x + 2 ) - 4( x + 2 ) = ( x + 2 )( x - 4 )

e) x2 - 5x - 6 = x2 + x - 6x - 6 = x( x + 1 ) - 6( x + 1 ) = ( x + 1 )( x - 6 )

f) x2 - 6x + 8 = x- 2x - 4x + 8 = x( x - 2 ) - 4( x - 2 ) = ( x - 2 )( x - 4 )

g) x2 + 4x + 3 = x2 + x + 3x + 3 = x( x + 1 ) + 3( x + 1 ) = ( x + 1 )( x + 3 )

h) x2 - 2x - 15 = x2 + 3x - 5x - 15 = x( x + 3 ) - 5( x + 3 ) = ( x + 3 )( x - 5 )

i) x2 + 7x + 12 = x2 + 3x + 4x + 12 = x( x + 3 ) + 4( x + 3 ) = ( x + 3 )( x + 4 )

j) x2 - 5x - 14 = x2 + 2x - 7x - 14 = x( x + 2 ) - 7( x + 2 ) = ( x + 2 )( x - 7 )

23 tháng 11 2017

a) \(x^2-y^2-5x-5y\)

\(=\left(x^2-y^2\right)-\left(5x+5y\right)\)

\(=\left(x-y\right)\left(x+y\right)-5\left(x+y\right)\)

\(=\left(x+y\right)\left(x-y-5\right)\)

b) \(5x^3-5x^2y-10x^2+10xy\)

\(=\left(5x^3-5x^2y\right)-\left(10x^2-10xy\right)\)

\(=5x^2\left(x-y\right)-10x\left(x-y\right)\)

\(=\left(x-y\right)\left(5x^2-10x\right)\)

\(=5x\left(x-y\right)\left(x-2\right)\)

c) \(x^3-2x^2-x+2\)

\(=\left(x^3-2x^2\right)-\left(x-2\right)\)

\(=x^2\left(x-2\right)-\left(x-2\right)\)

\(=\left(x-2\right)\left(x^2-1\right)\)

\(=\left(x-2\right)\left(x-1\right)\left(x+1\right)\)

d) \(-y^2+2xy-x^2+3x-3y\)

\(=-\left(y^2-2xy+x^2\right)+\left(3x-3y\right)\)

\(=-\left(y-x\right)^2+3\left(x-y\right)\)

\(=-\left(x-y\right)^2+3\left(x-y\right)\)

\(=\left(x-y\right)\left[-\left(x-y\right)+3\right]\)

\(=\left(x-y\right)\left(-x+y+3\right)\)

g) \(4x^2-8x+3\)

\(=4x^2-6x-2x+3\)

\(=\left(4x^2-6x\right)-\left(2x-3\right)\)

\(=2x\left(2x-3\right)-\left(2x-3\right)\)

\(=\left(2x-3\right)\left(2x-1\right)\)

h) \(2x^2-5x-7\)

\(=2x^2+2x-7x-7\)

\(=\left(2x^2+2x\right)-\left(7x+7\right)\)

\(=2x\left(x+1\right)-7\left(x+1\right)\)

\(=\left(x+1\right)\left(2x-7\right)\)

k) \(x^4+4\)

\(=x^4+4x^2+4-4x^2\)

\(=\left[\left(x^2\right)^2+2.x^2.2+2^2\right]-4x^2\)

\(=\left(x^2+2\right)^2-\left(2x\right)^2\)

\(=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)