a) 9x^2+6xy+y^2

=(3x+y)²

b)6x - 9 - x^2

=-(x²-6x+9)

=-(x-3)²

c) x^2 + 4y^2 + 4xy

=(x+2y)²

9x² + 6xy + y²

= (3x)² + 2.3x.y + y²

= (3x + y)²

b) 6x - 9 - x² 

= -(x² - 6x + 9)

= -(x - 3)²

mọi người nếu như có thể thì ghi cả cách lm ra hộ em vs ạ

bạn viết lại đề đi, có số mũ, xuống dòng chứ thế này ai mà giải được

a) Xem lại đề

b) x³ - 4x²y + 4xy² - 9x

= x(x² - 4xy + 4y² - 9)

= x[(x² - 4xy + 4y² - 3²]

= x[(x - 2y)² - 3²]

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

c) x³ - y³ + x - y

= (x³ - y³) + (x - y)

= (x - y)(x² + xy + y²) + (x - y)

= (x - y)(x² + xy + y² + 1)

d) 4x² - 4xy + 2x - y + y²

= (4x² - 4xy + y²) + (2x - y)

= (2x - y)² + (2x - y)

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

e) 9x² - 3x + 2y - 4y²

= (9x² - 4y²) - (3x - 2y)

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

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

f) 3x² - 6xy + 3y² - 5x + 5y

= (3x² - 6xy + 3y²) - (5x - 5y)

= 3(x² - 2xy + y²) - 5(x - y)

= 3(x - y)² - 5(x - y)

= (x - y)[(3(x - y) - 5]

= (x - y)(3x - 3y - 5)

a) = (x - 2)² - y²

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

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

= (x + 3)² - (2y)²

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

c) = (x - 3y)² - 6²

= (x - 3y - 6)(x - 3y + 6)

phân tích thành nhân tử: 

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

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

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

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

\(9x^2+6xy+y^2=\left(3x\right)^2+2\cdot3x\cdot1+y^2=\left(3x+y\right)^2\)

\(x^2+4y^2+4xy=x^2+2\cdot x\cdot2y+\left(2y\right)^2=\left(x+2y\right)^2\)

a. \(x^3-0.25x=0\Rightarrow x\left(x^2-\frac{1}{4}\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x^2-\frac{1}{4}=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x^2=\frac{1}{4}\end{cases}}}\) \(\Rightarrow\orbr{\begin{cases}x=0\\\orbr{\begin{cases}x=\frac{1}{2}\\x=\frac{-1}{2}\end{cases}}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=0\\\orbr{\begin{cases}x=\frac{1}{2}\\x=\frac{-1}{2}\end{cases}}\end{cases}}\)=> \(x\in\left\{0;\frac{1}{2};\frac{-1}{2}\right\}\)

b, \(x^2-10x=-25\)\(\Rightarrow x^2-10x+25=0\)

 \(\Rightarrow\left(x-5\right)^2=0\Rightarrow x-5=0\Rightarrow x=5\)

a, \(x^2-9=x^2-3x+3x-9\)

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

b, \(4x^2-25=\left(2x\right)^2-5^2=\left(2x-5\right)\left(2x+5\right)\)

c, \(x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2=\left(x^3+y^3\right)\left(x^3-y^3\right)\)

d, \(9x^2+6xy+y^2=\left(3x\right)^2+2\left(3xy\right)+y^2\) \(=\left(3x+y\right)^2\)

e, \(6x-9-x^2=6x-18+9-x^2\) \(=6\left(x-3\right)-\left(x-3\right)\left(x+3\right)\)

\(=\left(x-3\right)\left(6-x-3\right)=\left(x-3\right)\left(3-x\right)\)

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

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

\(\)

a)x³-6x²+9x=x(x²-6x+9)=x(x-3)²

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

c)x²-x+xy-y=x(x-1)+y(x-1)=(x-1)(x+y)

d)3x²-6xy-75+3y²=3[(x²-2xy+y²)-25]=3[(x-y)²-5²]=3(x-y-5)(x-y+5)

e)2x²-5x-7=(2x²+2x)-(7x+7)=2x(x+1)-7(x+1)=(x+1)(2x-7)

f)x⁴+36=x⁴+12x²+36-12x²=(x²+6)²-12x²=(x²-\(\sqrt{12}x\)+6)(x²+\(\sqrt{12}x\)+6)

h)x⁴+4y⁴=x⁴+4x²y²+4y²-4x²y²=(x²+2y²)-4x²y²=(x²+2y²-2xy)(x²+2y²+2xy)

a)\(6x-9-x^2\)

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

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

b)\(x^2+4y^2+4xy\)

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

c)\(x^2+8x+16\)

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

d)\(9x^2-12xy+4y^2\)

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

e)\(-25x^2y^2+10xy-1\)

\(=-\left(25x^2y^2-10xy+1\right)\)

\(=-\left(5xy-1\right)^2\)

f)\(4x^2-4x+1\)

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

j)\(x^2+6x+9\)

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

h)\(9x^2-6x+1\)

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

#H

a, 6x - 9 - x² = - x² + 6x - 9 = - (x² - 6x + 9) = - (x - 3)²

b, x² + 4y² + 4xy = x² + 2. x . 2y + (2y)² = (x + 2y)²

c, x² + 8x + 16 = x² + 2 . x . 4 + 4² = (x + 4)²

d, 9x² - 12xy + 4y² = (3x)² - 2 . 3x . 2y + (2y)² = (3x - 2y)²

e, - 25x²y² + 10xy - 1 = - (25x²y² - 10xy + 1) = - [(5xy)² - 2 . 5xy + 1] = - (5xy - 1)²

f, 4x² - 4x + 1 = (2x)² - 2 . 2x + 1 = (2x - 1)²

j, x² + 6x + 9 = x² + 2 . x . 3 + 3² = (x + 3)²

h, 9x² - 6x + 1 = (3x)² - 2 . 3x + 1 = (3x - 1)²

a: 2x^2y-50xy=2xy(x-25)

b: 5x^2-10x=5x(x-2)

c: 5x^3-5x=5x(x^2-1)=5x(x-1)(x+1)

d: \(x^2-xy+x=x\left(x-y+1\right)\)

e: x(x-y)-2(y-x)

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

=(x-y)(x+2)

f: 4x^2-4xy-8y^2

=4(x^2-xy-2y^2)

=4(x^2-2xy+xy-2y^2)

=4[x(x-2y)+y(x-2y)]

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

f1: x^2ỹ-y^2+y

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

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