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\(\begin{array}{l}A + B = \left( {5{x^2}y + 5x - 3} \right) + \left( {xy - 4{x^2}y + 5x - 1} \right)\\ = 5{x^2}y + 5x - 3 + xy - 4{x^2}y + 5x - 1\\ = \left( {5{x^2}y - 4{x^2}y} \right) + xy + \left( {5x + 5x} \right) + \left( { - 3 - 1} \right)\\ = {x^2}y + xy + 10x - 4\end{array}\)
a) \(\left(4x^4-8x^2y^2+12x^5y\right):\left(-4x^2\right)\)
\(=4x^4:-4x^2-8x^2y^2:-4x^2+12x^4y:-4x^2\)
\(=-x^2+2y^2-3x^2y\)
b) \(x^2\left(x-y^2\right)-xy\left(1-xy\right)-x^3\)
\(=x^3-x^2y^2-xy+x^2y^2-x^3\)
\(=-xy\)
a: \(=\dfrac{x^4-6x^3+12x^2-14x+3}{x^2-4x+1}\)
\(=\dfrac{x^4-4x^3+x^2-2x^3+8x^2-2x+3x^2-12x+3}{x^2-4x+1}\)
\(=x^2-2x+3\)
b: \(=\dfrac{x^5-3x^4+5x^3-x^2+3x-5}{x^2-3x+5}=x^2-1\)
c: \(=\dfrac{2x^4-5x^3+2x^2+2x-1}{x^2-x-1}\)
\(=\dfrac{2x^4-2x^3-2x^2-3x^3+3x^2+3x+x^2-x-1}{x^2-x-1}\)
\(=2x^2-3x+1\)
TL:
\(\left(x-y\right)\left(x^2+xy+y^2\right)\)
\(=x^3+x^2y+xy^2-yx^2-xy^2-y^3\)
\(=x^3-y^3\)
\(\left(x-y\right)\left(x^2+xy+y^2\right)\)
\(=x\left(x^2+xy+y^2\right)-y\left(x^2+xy+y^2\right)\)
\(=\left(x^3+x^2y+xy^2\right)-\left(x^2y+xy^2+y^3\right)\)
\(=x^3+x^2y+xy^2-x^2y-xy^2-y^3\)
\(=x^3-y^3\)
bài 11
a) \(x^2-xy+x\\ =x\left(x-y+1\right)\)
b)
\(x^2-2xy-4+y^2\\ =\left(x^2-2xy+y^2\right)-4\\ =\left(x-y\right)^2-4\\ =\left(x-y-2\right)\left(x-y+2\right)\)
c)
\(x^3-x^2-16x+16\\ =x^2\left(x-1\right)-16\left(x-1\right)\\ =\left(x-1\right)\left(x-4\right)\left(x+4\right)\)
bài 12
\(2x\left(x-5\right)-x\left(3+2x\right)=26\)
\(2x^2-10x-3x-2x^2=26\)
\(-13x=26\\ x=-2\)
b)
\(2\left(x+5\right)-x^2-5x=0\\ 2\left(x+5\right)-x\left(x+5\right)=0\\ \left(x+5\right)\left(2-x\right)=0\\ \left[{}\begin{matrix}x+5=0\\2-x=0\end{matrix}\right.\left[{}\begin{matrix}x=-5\\x=2\end{matrix}\right.\)
a, \(P=\left(5x-1\right)+2\left(1-5x\right)\left(4+5x\right)+\left(5x+4\right)^2\)
\(=5x-1+2\left(4+5x-20x-25x^2\right)+\left(25x^2+40x+16\right)\)
\(=5x-1+8-30x-50x^2+25x^2+40x+16\)
\(=\left(-50x^2+25x^2\right)+\left(5x-30x+40x\right)+\left(-1+8+16\right)\)
\(=-25x^2+15x+23\)
b, \(Q=\left(x-y\right)^3+\left(y+x\right)^3+\left(y-x\right)^3-3xy\left(x+y\right)\)
\(=x^3-3x^2y+3xy^2-y^3+y^3+3y^2x+3yx^2+x^3+y^3-3y^2x+3yx^2-x^3-3x^2y-3xy^2\)
\(=\left(x^3+x^3-x^3\right)+\left(-y^3+y^3+y^3\right)+\left(-3x^2y+3x^2y+3x^2y-3x^2y\right)+\left(3xy^2+3xy^2-3xy^2-3xy^2\right)\)
\(=x^3+y^3\)
Chúc bạn học tốt!!!
\(\begin{array}{l}A - B = \left( {5{x^2}y + 5x - 3} \right) - \left( {xy - 4{x^2}y + 5x - 1} \right)\\ = 5{x^2}y + 5x - 3 - xy + 4{x^2}y - 5x + 1\\ = \left( {5{x^2}y + 4{x^2}y} \right) - xy + \left( {5x + 5x} \right) + \left( { - 3 + 1} \right)\\ = 9{x^2}y - xy + 10x - 2\end{array}\)