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5 tháng 12 2017

 = (8x^2-2ax) + (4xy-ay)

 = 2x.(4x-a) + y.(4x-a) = (2x+y).(4x-a)

k mk nha

5 tháng 12 2017

=(8X2+4XY)-(2AX+AY)

=4X(2X+Y)-A(2X+Y)

=(2X+Y)(4X-A)

\(\left(2x-y\right)\left(4x^2-4xy+y^2\right)-8x^2\left(x-y\right)\)

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

\(=8x^3-12x^2y+6xy^2-y^3-8x^3+8x^2y\)

\(=-4x^2y-6xy^2-y^3\)

\(=-y\left(4x^2+6xy+y^2\right)\)

9 tháng 10 2021

\(ax^2+a-axy+2ax-ay\)

\(a\left(x^2+2x+1\right)-ay\left(x+1\right)\)

\(a\left(x+1\right)^2-ay\left(x+1\right)\)

\(\left(x+1\right)\left[a\left(x+1\right)-ay\right]\)

\(\left(x+1\right)\left(ax+a-ay\right)\)

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

1 tháng 10 2016

a) 8x2 + 4xy - 2ax - ay = (8x2 + 4xy) - (2ax + ay) = 4x(2x + y) - a(2x + y) = (4x - a)(2x + y)

b) 2xy - x2 - y2 = 16 - (-2xy + x2 + y2) = 42 - (x - y)2 = (4 - x + y)(4 + x - y)

c) x2 - y2 - 2yz - z2 = x2 - (y2 + 2yz + z2) = z2 - (y + z)2 = (z - y - z)(z + y + z)

AH
Akai Haruma
Giáo viên
10 tháng 8 2021

1.

$4x^2y+5x^3-x^2y^2=x^2(4y+5x-y^2)$

2.

$5x(x-1)-3y(1-x)=5x(x-1)+3y(x-1)=(x-1)(5x+3y)$

3.

$4x^2-25=(2x)^2-5^2=(2x-5)(2x+5)$

4.

$6x-9-x^2=-(x^2-6x+9)=-(x-3)^2$

5.

$x^2+4y^2+4xy=x^2+2.x.2y+(2y)^2=(x+2y)^2$

6.

$\frac{1}{64}-27x^3=(\frac{1}{4})^3-(3x)^3$
$=(\frac{1}{4}-3x)(\frac{1}{16}+\frac{3x}{4}+9x^2)$
 

AH
Akai Haruma
Giáo viên
10 tháng 8 2021

7.

$x^3-6x^2+12x-8=x^3-3.x^2.2+3.x.2^2-2^3$

$=(x-2)^3$
8.

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

$=(x+y)(x-y-1)$

9.

$5x-5y+ax-ay=5(x-y)+a(x-y)$

$=(x-y)(5+a)$

1 tháng 10 2021

`a)x^3-8x^2+16x`

`=x(x^2-8x+16)`

`=x(x-4)^2`

`b)x^2+4y^2+2x-4y-4xy-24`

`=(x-2y)^2+2(x-2y)-24`

`=(x-2y)^2-4(x-2y)+6(x-2y)-24`

`=(x-2y-4)(x-2y+6)`

`c)x^4+x^3-x^2-2x-2`

`=x^4-2x^2+x^3-2x+x^2-2`

`=x^2(x^2-2)+x(x^2-2)+x^2-2`

`=(x^2-2)(x^2+x+1)`

30 tháng 8 2021

-8x2 + 5x + 3

<=> -8x2 + 8x - 3x + 3

<=> 8x(x - 1) - 3(x - 1)

<=> (8x - 3)(x - 1)

30 tháng 8 2021

-8x2+5x+3

=−1(8𝑥2−5𝑥−3)

=−1(8𝑥2+3𝑥−8𝑥−3)

=−1(𝑥(8𝑥+3)−1(8𝑥+3))=−1(𝑥−1)(8𝑥+3)

\(8x^2+4x+4=4\left(2x^2+x+1\right)\)

14 tháng 8 2021

a) \(=\left(x+6y\right)\left(x-6y\right)-\left(x-6y\right)\)

\(=\left(x-6y\right)\left(x-6y-1\right)\)

b) \(=x\left(x^2-8x+16\right)\)

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

c) \(=2\left(x-y\right)^2-18\)

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

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

a: \(x^2-36y^2-x+6y\)

\(=\left(x-6y\right)\left(x+6y\right)-\left(x-6y\right)\)

\(=\left(x-6y\right)\left(x+6y-1\right)\)

b: \(x^3-8x^2+16x\)

\(=x\left(x^2-8x+16\right)\)

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

c: \(2x^2-4xy+2y^2-18\)

\(=2\left(x^2-2xy+y^2-9\right)\)

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

d: \(3x^2-7x-10\)

\(=3x^2+3x-10x-10\)

\(=3x\left(x+1\right)-10\left(x+1\right)\)

\(=\left(x+1\right)\left(3x-10\right)\)

a: Ta có: \(x^2-36y^2-x+6y\)

\(=\left(x-6y\right)\left(x+6y\right)-\left(x-6y\right)\)

\(=\left(x-6y\right)\left(x+6y-1\right)\)

b: Ta có: \(16x-8x^2+x^3\)

\(=x\left(x^2-8x+16\right)\)

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

c: Ta có: \(2x^2-4xy+2y^2-18\)

\(=2\left(x^2-2xy+y^2-9\right)\)

\(=2\cdot\left[\left(x-y\right)^2-9\right]\)

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

d: Ta có: \(3x^2-7x-10\)

\(=3x^2+3x-10x-10\)

\(=3x\left(x+1\right)-10\left(x+1\right)\)

\(=\left(x+1\right)\left(3x-10\right)\)

e: Ta có: \(x^4-x^2-30\)

\(=x^4-6x^2+5x^2-30\)

\(=x^2\left(x^2-6\right)+5\left(x^2-6\right)\)

\(=\left(x^2-6\right)\left(x^2+5\right)\)

f: Ta có: \(x^2-xy-2y^2\)

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

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

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

g: Ta có: \(x^4-13x^2y^2+4y^4\)

\(=x^4-4x^2y^2+4y^4-9x^2y^2\)

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

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

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

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

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

h: Ta có: \(\left(x^2-2x\right)^2-2\left(x^2-2x\right)-3\)

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

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

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

\(=\left(x-3\right)\left(x+1\right)\cdot\left(x-1\right)^2\)