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

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

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

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

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

4 x 2 –   4 x y = 4 x x − y

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

b: =3x(x-y)-(x-y)=(x-y)(3x-1)

Bạn thử xem lại đề câu d nhé.

a) Ta có: \(4x\left(2x-3y\right)-8y\left(3y-2x\right)\)

\(=4x\left(2x-3y\right)+8y\left(2x-3y\right)\)

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

b) Ta có: \(4x^2-4xy+y^2-9z^2\)

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

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

c) Ta có: \(x^2y+yz+xy^2+xz\)

\(=xy\left(x+y\right)+z\left(x+y\right)\)

\(=\left(x+y\right)\left(xy+z\right)\)

Lời giải:

a. $3x^2-9x=3x(x-3)$

b. $4x^2+7y-4xy-7x=(4x^2-4xy)-(7x-7y)=4x(x-y)-7(x-y)=(x-y)(4x-7)$

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

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

a) $4x^2+4x+1$

$=(2x)^2+2\cdot2x\cdot1+1^2$

$=(2x+1)^2$

b) $x^2+6x-y^2+9$

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

$=(x^2+2\cdot x\cdot3+3^2)-y^2$

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

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

$\text{#}Toru$

a: \(4x^2+4x+1\)

\(=\left(2x\right)^2+2\cdot2x\cdot1+1^2\)

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

b: \(x^2+6x-y^2+9\)

\(=\left(x^2+6x+9\right)-y^2\)

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

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

1b.=2((x+y)+(x+y)(x-y)+(x-y))=2(x²-y²+x+y+x-y)=2(x²-y²+2x)=2x²-2y²+4x

2a.=4xy+4xy+2y=8xy+2y=2y(4x+1)

b.=(3x)²+2.3x.y+y²-(2z)²=(3x+y)²-(2z)²=(3x+y-2z)(3x+y+2z)

c.=x²-x-7x+7=x(x-1)-7(x-1)=(x-1)(x-7)

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

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

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

\(=4x^2\)

hk tốt

^^

b) 4x2 - 25 + (2x + 5)2

= (2x + 5)(2x - 5) + (2x + 5)2

= (2x + 5)(2x - 5 + 2x + 5)

= 4x(2x + 5)