Cm hệ số bất định
a) \(5y^{10}+15y^6\)
b) \(9x^2y^2+15x^2y-21xy^2\)
c) \(9\left(x+5\right)^2-\left(x-7\right)^2\)
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phân tích thành nhân tử
a) 4x^3 - 14x^2
b) 5y^10 + 15y^6
c) 9x^2 + 15x^2y - 21xy
d) 10x(x-y)-8y(y-x)
a) \(4x^3-14x^2\)
\(=2x^2\left(2x-7\right)\)
b) \(5y^{10}+15y^6\)
\(=5y^6\left(y^4+3\right)\)
c) \(9x^2+15x^2y-21xy\)
\(=3x\left(3x+5xy-7y\right)\)
d) \(10x\left(x-y\right)-8y\left(y-x\right)\)
\(=10x\left(x-y\right)+8y\left(x-y\right)\)
\(=\left(x-y\right)\left(10x+8y\right)\)
\(=2\left(x-y\right)\left(5x+4y\right)\)
\(a,4x^3-14x^2\)
\(=2x^3.2x-2x^3.7\)
\(2x^2\left(2x-7\right)\)
\(b,5y^{10}+15y^6\)
\(5y^6.y^4+5y^6.3\)
\(=5y^6\left(y^4+3\right)\)
\(c,9x^2+15x^2y-21xy\)
\(=3x\left(3x+5xy-7y\right)\)
\(d,10x\left(x-y\right)-8y\left(y-x\right)\)
\(=10x\left(x-y\right)+8y\left(x-y\right)\)
\(=\left(x-y\right)\left(10x+8y\right)\)
\(=2\left(x-y\right)\left(5x+4y\right)\)
a: \(=3y^2-5x^2y^3-2y^2+3x^2y^3=y^2-2x^2y^3\)
b: \(=6x-y+2x^2+3y^2-2x^2+x=7x-y+3y^2\)
c: \(=x-y+4y^2-6xy+\dfrac{10x^2}{y}\)
\(a.\left(9x^2y^3-15x^4y^4\right):3x^2y-\left(2-3x^2y\right)y^2\)
\(=3y^2-5x^2y^3-2y^2+3x^2y^3\)
\(=y^2-2x^2y^3\)
\(b.\left(6x^2-xy\right):x+\left(2x^3y+3xy^2\right):xy-\left(2x-1\right)x\)
\(=6x-y+2x^2+3y-2+x\)
\(=2x^2+7x+2y-2\)
\(c.\left(x^2-xy\right):x+\left(6x^2y^5-9x^3y^4+15x^4y^3\right):\dfrac{3}{2}x^2y^3\)
\(=x-y+4y^2-6xy+10x^2\)
\(\left(-z^2y^4\right)^2+\left(-\dfrac{2}{5}z^2y\right)\cdot\left(5x^2y^7\right)\cdot\left(\dfrac{4}{5}x^2y^5\right)^0-\left(\dfrac{9}{10}z^5y^7-z^4y^8\right)\\ =-z^4y^8-\dfrac{2}{5}z^2y\cdot5x^2y^7\cdot1-\dfrac{9}{10}z^5y^7+z^4y^8\\ =\left(-z^4y^8+z^4y^8\right)-2z^2x^2y^8-\dfrac{9}{10}z^5y^7\\ =-2x^2y^8z^2-\dfrac{9}{10}z^5y^7\)
a: \(=\dfrac{27a^6b^3\cdot a^2b^6}{a^8b^8}=27b\)
b: \(=3y^2-5x^2y^3-2y^2+3x^2y^3\)
\(=y^2-2x^2y^3\)
c: \(=6x-y+2x^2+3y-2x^2+x\)
\(=7x+2y\)
d: \(=x-y+2y^2-6xy+\dfrac{10x^2}{y}\)
a.x2-7x+10
⇔x2-2x-5x+10
⇔x(x-2)-5(x-2)
⇔(x-2)(x-5)
b.\(\left(12x^6y^4+9x^5y^3-15x^2y^3\right):3x^2y^3\)
=\(4x^4y+3x^3-5\)
=
x2-7x+10
= x2-5x-2x+10
=x(x-5)-2(x-5)
=(x-5)(x-2)
(12x6y4+9x5y3-15x2y3): 3x2y3
=4x4y+3x3-3
a) \(x+2y+\left(x-y\right)\)
\(=x+2y+x-y\)
\(=2x+y\)
b) \(2x+y-\left(3x-5y\right)\)
\(=2x+y-3x+5y\)
\(=-x+6y\)
c) \(3x^2-4y^2+6xy+7+\left(-x^2+y^2-8xy+9x+1\right)\)
\(=3x^2-4y^2+6xy+7-x^2+y^2-8xy+9x+1\)
\(=2x^2-3y^2-2xy+9x+8\)
d) \(4x^2y-2xy^2+8-\left(3x^2y+9xy^2-12xy+6\right)\)
\(=4x^2y-2xy^2+8-3x^2y-9xy^2+12xy-6\)
\(=x^2y-11xy^2+2+12xy\)
c,9(x+5)2-(x-7)2
<=>(3x+15)2-(x-7)2
<=>(3x+15+x-7)(3x+15-x+7)
<=>(4x+8)(2x+22)
<=>8(x+2)(x+11)