Phân tích đa thức thành nhân tử
x^2-y^2+8x+6y+7
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\(x^3-4x^2+8x-8=x^2\left(x-2\right)-2x\left(x-2\right)+4\left(x-2\right)=\left(x-2\right)\left(x^2-2x+4\right)\)
\(x^3-4x^2+8x-8\)
\(=\left(x-2\right)\left(x^2+2x+4\right)-4x\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2-2x+4\right)\)
x³ - 3x²y + 3xy² - y³ - z³
= (x³ - 3x²y + 3xy² - y³) - z³
= (x - y)³ - z³
= (x - y - z)[(x - y)² + (x - y)z + z²]
= (x - y - z)(x² - 2xy + y² + xz - yz + z³)
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x² - y² + 8x + 6y + 7
= (x² + 8x + 16) - (y² - 6y + 9)
= (x + 4)² - (y - 3)²
= (x + 4 - y + 3)(x + 4 + y - 3)
= (x - y + 7)(x + y + 1)
a: \(=\left(x^3-3x^2y+3xy^2-y^3\right)-z^3\)
\(=\left(x-y\right)^3-z^3\)
\(=\left(x-y-z\right)\left[\left(x-y\right)^2+z\left(x-y\right)+z^2\right]\)
\(=\left(x-y-z\right)\left(x^2-2xy+y^2+xz-yz+z^2\right)\)
b: \(=x^2+8x+16-y^2+6y-9\)
=(x+4)^2-(y-3)^2
=(x+4+y-3)(x+4-y+3)
=(x+y+1)(x-y+7)
a)\(=3x\left(x+2y\right)\)
c)\(=\left(x-7\right)\left(x-1\right)\)
b)\(=x\left(x-2y\right)+3\left(x-2y\right)=\left(x+3\right)\left(x-2y\right)\)
d)\(=\left(2x\right)^2-y^2=\left(2x-y\right)\left(2x+y\right)\)
\(a,3x^2+6xy=3x\left(x+2y\right)\\ c,x^2-8x+7=\left(x^2-x\right)-\left(7x-7\right)=x\left(x-1\right)-7\left(x-1\right)=\left(x-1\right)\left(x-7\right)\\ b,x^2-2xy+3x-6y=\left(x^2+3x\right)-\left(2xy+6y\right)=x\left(x+3\right)-2y\left(x+3\right)=\left(x+3\right)\left(x-2y\right)\\ d,4x^2-y^2=\left(2x-y\right)\left(2x+y\right)\)
\(x-y-\sqrt{x}-\sqrt{y}\\ =x-y-\left(\sqrt{x}+\sqrt{y}\right)\\ =\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)-\left(\sqrt{x}+\sqrt{y}\right)\\ =\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}-1\right)\)
=(x-y)-(căn x+căn y)
=(căn x-căn y)(căn x+căn y)-(căn x+căn y)
=(căn x+căn y)(căn x-căn y-1)
\(x^2\left(x-3\right)-4x+12=\left(x-3\right)\left(x-2\right)\left(x+2\right)\)
=x²(x-3)-4x+3.4
=x²(x-3)-4(x+3)
=x²(x-3)+4(x-3)
=(x-3)(x²+4)
=(x-3)(x²+2²)
=(x-3)(x-2)(x+2)
\(x^2-y^2+8x+6y+7\)
\(=\left(x-y\right)\left(x+y\right)+7\left(x+y\right)+x-y+7\)
\(=\left(x+y\right)\left(x-y+7\right)+\left(x-y+7\right)\)
\(=\left(x+y+1\right)\left(x-y+7\right)\)
Ta có x2 - y2 + 8x + 6y + 7
= x2 + 8x + 16 - y2 + 6y - 9
= \(x^2+4x+4x+16-y^2+3y+3y-9\)
= x(x + 4) + 4(x + 4) - y(y - 3) + 3(y - 3)
= (x + 4)2 - (y - 3)2
= (x + 4 + y - 3)(x + 4 - y + 3)
= (x + y + 1)(x - y + 7)