P(x)+Q(x)

=3x^2y-2x+5xy^2-7y^2+3xy^2-7y^2-9x^2y-x-5

=8xy^2-14y^2-6x^2y-3x-5

=>Chọn A

\(\hept{\begin{cases}3x^2-2y^2-xy+12x-17y-15=0\left(1\right)\\\sqrt{2-x}+\sqrt{6-x-x^2}=y+\sqrt{2y+5}-\sqrt{y+4}\left(2\right)\end{cases}}\)

PT (1) \(\Leftrightarrow3x^2-x\left(y-12\right)-2y^2-17y-15=0\)

\(\Leftrightarrow\Delta=\left(y-12\right)^2+4\cdot3\cdot\left(2y^2+17y+15\right)\)

\(\Leftrightarrow\Delta=y^2-24y+144+24y^2+204y+180\)

\(\Leftrightarrow\Delta=25y^2+180y+324\)

\(\Delta=\left(5y+18\right)^2\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{y-12+5y+18}{3}=2y+2\\x=\frac{y-12-5y-18}{3}=\frac{-4y}{3}-10\end{cases}}\)

\(x=2y+2\)

\(\Leftrightarrow\sqrt{2-x}+\sqrt{6-x-x^2}=y+\sqrt{2y+5}-\sqrt{y+4}\)

\(\Leftrightarrow\sqrt{-2y}+\sqrt{6-2y-2-4y^2-8y-4}=y+\sqrt{2y+5}-\sqrt{y+4}\)

\(\Leftrightarrow\sqrt{-2y}+\sqrt{-4y^2-10y+0}=y+\sqrt{2y+5}-\sqrt{y+6}\)

\(\Leftrightarrow y=0\Rightarrow x=2\)

Vậy (x;y)=(2;0)

a/ Ta có \(\sqrt{x^2-6x+22}+\sqrt{x^2-6x+10}=4\)

\(\Leftrightarrow\left(\sqrt{x^2-6x+22}+\sqrt{x^2-6x+10}\right)\left(\sqrt{x^2-6x+22}-\sqrt{x^2-6x+10}\right)=4A\)

\(\Leftrightarrow4A=\left(x^2-6x+22\right)-\left(x^2-6x+10\right)\)

\(\Leftrightarrow4A=12\Leftrightarrow A=3\)

b/ Tương tự.

a) 3x³ + 6x²y

= 3x².(x + 2y)

b) 2x³ - 6x²

= 2x².(x - 2)

c) 18x² - 20xy

= 2x.(9x - 10y)

d) xy + y² - x - y

= (xy + y²) - (x + y)

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

= (x + y)(y - 1)

e) (x²y² - 8)² - 1

= (x²y² - 8 - 1)(x²y² - 8 + 1)

= (x²y² - 9)(x²y² - 7)

= (xy - 3)(xy + 3)(x²y² - 7)

f) x² - 7x - 8

= x² - 8x + x - 8

= (x² - 8x) + (x - 8)

= x(x - 8) + (x - 8)

= (x - 8)(x + 1)

a: \(3x^3+6x^2y\)

\(=3x^2\cdot x+3x^2\cdot2y=3x^2\left(x+2y\right)\)

b: \(2x^3-6x^2=2x^2\cdot x-2x^2\cdot3=2x^2\left(x-3\right)\)

c: \(18x^2-20xy=2x\cdot9x-2x\cdot10y=2x\left(9x-10y\right)\)

d: \(xy+y^2-x-y\)

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

\(=\left(x+y\right)\left(y-1\right)\)

e: \(\left(x^2y^2-8\right)^2-1\)

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

\(=\left(x^2y^2-7\right)\left(x^2y^2-9\right)\)

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

f: \(x^2-7x-8\)

\(=x^2-8x+x-8\)

\(=x\left(x-8\right)+\left(x-8\right)=\left(x-8\right)\left(x+1\right)\)

g: \(10x^2\left(2x-y\right)+6xy\left(y-2x\right)\)

\(=2x\cdot\left(2x-y\right)\cdot5x-2x\cdot\left(2x-y\right)\cdot3y\)

\(=2x\left(2x-y\right)\left(5x-3y\right)\)

h: \(x^2-2x+1-y^2\)

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

\(=\left(x-1-y\right)\left(x-1+y\right)\)

i: \(2x\left(x+2\right)+x^2\left(-x-2\right)\)

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

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

\(=-\left(x^2-2\cdot x\cdot3+3^2\right)=-\left(x-3\right)^2\)

l: \(-2x^2+8xy-8y^2\)

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

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

m: \(3x^2+5x-3y^2-5y\)

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

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

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

g) 10x²(2x - y) + 6xy(y - 2x)

= 10x²(2x - y) - 6xy(2x - y)

= 2x(2x - y)(5x - 3y)

h) x² - 2x + 1 - y²

= (x² - 2x + 1) - y²

= (x - 1)² - y²

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

i) 2x(x + 2) + x² (-x - 2)

= 2x(x + 2) - x²(x + 2)

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

k) -9 + 6x - x²

= -(x² - 6x + 9)

= -(x - 3)²

l) 8xy - 2x² - 8y²

= -2(x² - 4xy + 4y²)

= -2(x - 2y)²

m) 3x² + 5x - 3y² - 5y

= (3x² - 3y²) + (5x - 5y)

= 3(x² - y²) + 5(x - y)

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

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

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