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

\(=9x^4-6x^2y^2-9x^4+4y^4\)

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

Cảm ơn bạn nhiều nha

3: \(x^4-13x^2+36\)

\(=x^4-9x^2-4x^2+36\)

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

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

4: \(x^4+3x^2-2x+3\)

\(=x^4+x^3+3x^2-x^3-x^2-3x+x^2+x+3\)

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

5: \(x^4+2x^3+3x^2+2x+1\)

\(=x^4+x^3+x^2+x^3+x^2+x+x^2+x+1\)

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

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

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

\(\Leftrightarrow2y^2\cdot\left(3x^2-2y^2\right)\)

\(\Leftrightarrow6x^2y^2-4y^4\)

\(2y^2\cdot2y^2=4y^4\) đúng rồi còn gì, lấy đâu ra x

`A= x^2+2xy-3x^2 +2y^2+3x^2-y^2`

`= (x^2-3x^2 +3x^2) +2xy +(2y^2 -y^2)`

`= x^2 +2xy +y^2`

`=(x+y)^2`

A = \(x^2\) + 2\(xy\) - 3\(x^2\) + 2y² + 3\(x^2\) - y²

A = (\(x^2\)- 3\(x^2\) + 3\(x^2\)) + 2\(xy\) + (2\(y^2\) - y²)

A = \(x^2\) + 2\(xy\) + y²

A = (\(x\) + y)²

\(a,9x^2+y^2+2z^2-18x+4z-6y+20=0\\ \Leftrightarrow9\left(x-1\right)^2+\left(y-3\right)^2+2\left(z+1\right)^2=0\\ \Leftrightarrow\left\{{}\begin{matrix}x=1\\y=3\\z=-1\end{matrix}\right.\)

\(b,5x^2+5y^2+8xy+2y-2x+2=0\\ \Leftrightarrow4\left(x+y\right)^2+\left(x-1\right)^2+\left(y+1\right)^2=0\\ \Leftrightarrow\left\{{}\begin{matrix}x=-y\\x=1\\y=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-1\end{matrix}\right.\)

\(c,5x^2+2y^2+4xy-2x+4y+5=0\\ \Leftrightarrow\left(2x+y\right)^2+\left(x-1\right)^2+\left(y+2\right)^2=0\\ \Leftrightarrow\left\{{}\begin{matrix}2x=-y\\x=1\\y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-2\end{matrix}\right.\)

\(d,x^2+4y^2+z^2=2x+12y-4z-14\\ \Leftrightarrow\left(x-1\right)^2+\left(2y-3\right)^2+\left(z+2\right)^2=0\\ \Leftrightarrow\left\{{}\begin{matrix}x=1\\y=\dfrac{3}{2}\\z=-2\end{matrix}\right.\)

\(e,x^2+y^2-6x+4y+2=0\\ \Leftrightarrow\left(x-3\right)^2+\left(y+2\right)^2=11\)

Pt vô nghiệm do ko có 2 bình phương số nguyên có tổng là 11

e: Ta có: \(x^2-6x+y^2+4y+2=0\)

\(\Leftrightarrow x^2-6x+9+y^2+4y+4-11=0\)

\(\Leftrightarrow\left(x-3\right)^2+\left(y+2\right)^2=11\)

Dấu '=' xảy ra khi x=3 và y=-2

2:

a: \(3xy^2-3x^3-6xy+3x\)

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

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

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

b: \(3x^2+11x+6\)

\(=3x^2+9x+2x+6\)

=3x(x+3)+2(x+3)

=(x+3)(3x+2)

c: \(-x^3-4xy^2+4x^2y+16x\)

\(=x\left(16+4xy-4y^2-x^2\right)\)

\(=x\cdot\left\lbrack4^2-\left(x^2-4xy+4y^2\right)\right\rbrack=x\cdot\left\lbrack4^2-\left(x-2y\right)^2\right\rbrack\)

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

d: \(xz-x^2-yz+2xy-y^2\)

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

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

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

e: \(4x^2-y^2-6x+3y\)

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

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

f: \(x^4-x^3-10x^2+2x+4\)

\(=x^4+2x^3-2x^2-3x^3-6x^2+6x-2x^2-4x+4\)

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

g: \(\left(x^3-x^2+x\right)\left(121-25y^2-10y\right)-\left(x^3-x^2+x\right)-\left(121-25y^2-10y\right)+1\)

\(=\left(x^3-x^2+x\right)\left(121-25y^2-10y-1\right)-\left(121-25y^2-10y-1\right)\)

\(=\left(x^3-x^2+x-1\right)\left\lbrack121-\left(25y^2+10y+1\right)\right\rbrack\)

\(=\left(x-1\right)\left(x^2+1\right)\left\lbrack121-\left(5y+1\right)^2\right\rbrack\)

=(x-1)(x^2+1)(11-5y-1)(11+5y+1)

=(x-1)(x^2+1)(10-5y)(12+5y)

=5(2-y)(x-1)(x^2+1)(5y+12)

a) Ta có: \(\dfrac{6x^2-8xy}{9xy-12y^2}\)

\(=\dfrac{2x\left(3x-4y\right)}{3y\left(3x-4y\right)}=\dfrac{2x}{3y}\)
b) \(\dfrac{2a^3-18a}{a^4-81}\)

\(=\dfrac{2a\left(a^2-9\right)}{\left(a^2-9\right)\left(a^2+9\right)}=\dfrac{2a}{a^2+9}\)

a) Ta có:

\(A+B\)

\(=3x^2-9xy+y^2-7-y^2-3x+12\)

\(=3x^2-9xy+5-3x\)

b) Ta có:

\(A-B\)

\(=\left(3x^2-9xy+y^2-7\right)-\left(-y^2-3x+12\right)\)

\(=3x^2-9xy+y^2-7+y^2+3x-12\)

\(=3x^2-9xy+2y^2+3x-19\)

a) \(a+b=\left(3x^2-9xy+y^2\right)+\left(-y^2-3x+12\right)\)

\(=3x^2-9xy+y^2-y^2-3x+12\)

\(=3x^2-9xy+\left(y^2-y^2\right)-3x+12\)

\(=3x^2-9xy-3x+12\)

b) \(a-b=\left(3x^2-9xy+y^2\right)-\left(-y^2-3x+12\right)\)

\(=3x^2-9xy+y^2+y^2+3x-12\)

\(=3x^2-9xy+\left(y^2+y^2\right)+3x-12\)

\(=3x^2-9xy+2y^2+3x-12\)