3x(\(^{x^2-6xy+9y^2}\))

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

câu b sai r 

\(\dfrac{1}{3}xy+x^2z+xz=3x\left(\dfrac{1}{9}y+\dfrac{1}{3}xz+\dfrac{1}{3}z\right)\)

Lời giải:

a.

$=\frac{1}{2}(x^2-4y^2)=\frac{1}{2}[x^2-(2y)^2]=\frac{1}{2}(x-2y)(x+2y)$

b.

$=\frac{1}{3}x(y+3xz+3z)$

c.

$=\frac{2}{25}x(225x^2-4)=\frac{2}{25}(15x-2)(15x+2)$

d.

$=\frac{1}{5}x^2(2+25x+5y)$

a: Ta có: \(10x^4-27x^3y-110x^2y^2-27xy^3+10y^4\)

\(=10x^4+20x^2y^2+10y^4-27xy\left(x^2+y^2\right)-130x^2y^2\)

\(=10\left(x^2+y^2\right)^2-27xy\left(x^2+y^2\right)-130x^2y^2\)

\(=10\left(x^2+y^2\right)^2-52xy\left(x^2+y^2\right)+25xy\left(x^2+y^2\right)-130x^2y^2\)

\(=2\left(x^2+y^2\right)\left(5x^2+5y^2-26xy\right)+5xy\left(5x^2+5y^2-26xy\right)\)

\(=\left(5x^2-26xy+5y^2\right)\left(2x^2+5xy+2y^2\right)\)

\(=\left(5x^2-25xy-xy+5y^2\right)\left(2x^2+4xy+xy+2y^2\right)\)

\(=\left\lbrack5x\left(x-5y\right)-y\left(x-5y\right)\right\rbrack\left\lbrack2x\left(x+2y\right)+y\left(x+2y\right)\right\rbrack\)

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

b: \(x^5-4x^4+3x^3+3x^2-4x+1\)

\(=x^5+x^4-5x^4-5x^3+8x^3+8x^2-5x^2-5x+x+1\)

\(=\left(x+1\right)\left(x^4-5x^3+8x^2-5x+1\right)\)

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

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

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

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

a: \(\frac12x^2-2y^2=\frac12\left(x^2-4y^2\right)\)

\(=\frac12\left(x-2y\right)\left(x+2y\right)\)

b: \(\frac13xy+x^2z+xz\)

\(=x\cdot\frac13y+x\cdot xz+x\cdot z\)

\(=x\left(\frac13y+xz+z\right)\)

c: \(18x^3-\frac{8}{25}x=2x\left(9x^2-\frac{4}{25}\right)\)

\(=2x\left\lbrack\left(3x\right)^2-\left(\frac25\right)^2\right\rbrack\)

\(=2x\left(3x-\frac25\right)\left(3x+\frac25\right)\)

d: \(\frac25x^2+5x^3+x^2y=x^2\cdot\frac25+x^2\cdot5x+x^2\cdot y=x^2\left(\frac25+5x+y\right)\)

e: \(\frac12\left(x^2+y^2\right)^2-2x^2y^2\)

\(=\frac12\left\lbrack\left(x^2+y^2\right)^2-4x^2y^2\right\rbrack\)

\(=\frac12\left(x^2+y^2-2xy\right)\left(x^2+y^2+2xy\right)\)

\(=\frac12\left(x-y\right)^2\cdot\left(x+y\right)^2\)

f: \(27x^3-\frac18y^3=\left(3x\right)^3-\left(\frac12y\right)^3\)

\(=\left(3x-\frac12y\right)\left(9x^2+\frac32xy+\frac14y^2\right)\)

a) \(x^2yz+4zyx+4yz\)

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

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

b) \(5x^4-3x^3y-45x^2y^2+27xy^3\)

\(=x\left(5x^3-3x^2y-45xy^2+27y^3\right)\)

v

lẹ

gấp

Mày ra câu hỏi từ từ người ta trả lới cho chứ cứ hối người ta 😡

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

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

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

b) \(x^3-x+3x^2y+3xy^2+y^3-y\)

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

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

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

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

1D  2C

Câu 1: D

Câu 2: C