\(9x^2y^2+15x^2y-21xy^2\\ =3xy\left(3xy+5x-7y\right)\)

Ta có: \(9x^2y^2+15x^2y-21xy^2\)

\(=3xy\left(3xy+5x-7y\right)\)

d: \(=\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)

gọi đa thức cần diền vào chỗ (...) là a

`=>11x^2y-a=15x^2y+1`

`=>a=11x^2y-15x^2y-1`

`=>a=-1-4x^2y`

Vậy đa thức cần điền là `-1-4x^2`y

a) \(x^3+3x=x\left(x+3\right)\)

b) \(9x^2-6x=3x\left(3x-2\right)\)

c) \(5y^{10}+15y^6=5y^6\left(y^4+3\right)\)

d) \(x^4y-2x^2y^2+5xy=xy\left(x^3-2xy+5\right)\)

f: \(\left(y-1\right)^2\)

e: =(x+y+5)(x+y-5)

\(d,15x^2y+20xy^2+25xy=5xy\left(3x+4y+5\right)\\ e,\left(x+y\right)^2-25=\left(x+y\right)^2-5^2=\left(x+y-5\right)\left(x+y+5\right)\\ f,1-2y+y^2=\left(1-y\right)^2\\ h,4x^2+8xy-3x-6y=\left(4x^2+8xy\right)-\left(3x+6y\right)=4x\left(x+2y\right)-3\left(x+2y\right)=\left(x+2y\right)\left(4x-3\right)\)

\(=xy\left(4x-21y+28xy\right)\)

\(x\left(9xy^2-4\right)\)

 9x²y²-4x

= x(9xy²−4)

\(\left(3x^3y^2-9x^2y^2+15xy^3\right):3xy^2\)

\(=3x^3y^2:3xy^2-9x^2y^2:3xy^2+15xy^3:3xy^2\)

\(=\left(3:3\right)\cdot x^{3-1}\cdot y^{2-2}-\left(9:3\right)\cdot x^{2-1}\cdot y^{2-2}+\left(15:3\right)\cdot x^{1-1}\cdot y^{3-2}\)

\(=x^2-3x+5y\)

\(\left(3x^4y^3-9x^2y^2+25xy^3\right):xy^2-3x^3y+9x+25\) 

\(=3x^4y^3:xy^3-9x^2y^2:xy^2+25xy^3:xy^2-3x^3y-9x+25\)

\(=3x^3-9x+25y-3x^3y-9x+25\)

\(=3x^3-18x+25y-3x^3y+25\)

\(A=\left(\dfrac{3}{4}x^4y^2-\dfrac{9}{2}x^3y^2+9x^2y^2\right):\dfrac{3}{4}xy^2\)

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

\(=1^3-6\cdot1^2+12\cdot1=1+12-6=13-6=7\)