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\(x^3+8y^3+2xy^2+x^2y\)
\(=x^3+2x^2y-x^2y-2xy^2+4xy^2+8y^3\)
\(=x^2\left(x+2y\right)-xy\left(x+2y\right)+4y^2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x^2-xy+4y^2\right)\)
\(1-2y+y^2=\left(y-1\right)^2\)
\(\left(x+1\right)^2-25=\left(x-1\right)^2-5^2=\left(x-6\right)\left(x+4\right)\)
\(1-4x^2=1-\left(2x\right)^2=\left(1-2x\right)\left(1+2x\right)\)
\(8-27x^3=\left(2-3x\right)\left(4+6x+9x^2\right)\)
\(27+27x+9x^2+x^3=\left(x+3\right)^3\)
\(8x^3-12x^2y+6xy^2-y^3=\left(2x-y\right)^3\)
\(x^3+8y^3=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)
Tham khảo nhé~
Mấy cái này chỉ áp dụng HĐT thoyy nha!
\(a,1-2y+y^2=\left(1-y\right)^2\)
\(b,\left(x-1\right)^2-25=\left(x-1-5\right)\left(x-1+5\right)=\left(x-6\right)\left(x+4\right)\)
\(c,1-4x^2=\left(1-2x\right)\left(1+2x\right)\)
\(d,8-27x^3=\left(2-3x\right)\left(4+6x+9x^2\right)\)
\(e,27+27x+9x^2+x^3=\left(x+3\right)^3\)
\(f,8x^3-12x^2y+9xy^2-y^3=\left(2x-y\right)^2\)
\(g,x^3+8y^3=\left(x+2y\right)\left(x^2-2xy+y^2\right)=\left(x+2y\right)\left(x-y\right)^2\)
=.= hok tốt!!
a: 2x^2y-50xy=2xy(x-25)
b: 5x^2-10x=5x(x-2)
c: 5x^3-5x=5x(x^2-1)=5x(x-1)(x+1)
d: \(x^2-xy+x=x\left(x-y+1\right)\)
e: x(x-y)-2(y-x)
=x(x-y)+2(x-y)
=(x-y)(x+2)
f: 4x^2-4xy-8y^2
=4(x^2-xy-2y^2)
=4(x^2-2xy+xy-2y^2)
=4[x(x-2y)+y(x-2y)]
=4(x-2y)(x+y)
f1: x^2ỹ-y^2+y
=(x-y)(x+y)+(x+y)
=(x+y)(x-y+1)
a) 5x^2 + 6xy + y^2
=5x2+5xy+xy+y2
=5x.(x+y)+y.(x+y)
=(x+y)(5x+y)
b) x^2 + 2xy - 15y^2.
=x2-3xy+5xy-15y2
=x.(x-3y)+5y.(x-3y)
=(x-3y)(x+5y)
c) (x-y)^2 + 4(x-y) - 12
=(x-y)2+4(x-y)+4-16
=(x-y+2)2-16
=(x-y+2-4)(x-y+2+4)
=(x-y-2)(x-y+6)
d) x^3 - 2x - 4.
=x3+2x2+2x-2x2-4x-4
=x.(x2+2x+2)-2.(x2+2x+2)
=(x2+2x+2)(x-2)
a);b);c) Dùng máy tính (cụ thể là solve) bấm nghiệm rồi phân tích
d)Nhóm số T1;T2;T4 lại vs nhau
e)Biến đổi thành x2-2xy+y2-9y2
a) \(x^4+x^3+2x^2+x+1=\left(x^4+x^3+x^2\right)+\left(x^2+x+1\right)\)
\(=x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^2+1\right)\)
b) \(4x^2-4x-3=4x^2+2x-6x-3=2x\left(2x+1\right)-3\left(2x+1\right)=\left(2x+1\right)\left(2x+3\right)\)
c) \(4x^4+81=4x^4+36x^2+81-36x^2\)
\(=\left(2x^2+9\right)^2-36x^2=\left(2x^2-6x+9\right)\left(2x^2+6x-9\right)\)
d) \(x^2-6xy-25+9y^2=\left(x-3y\right)^2-25=\left(x-3y-5\right)\left(x-3y+5\right)\)
e) \(x^2-8y^2-2xy=x^2+2xy-4xy-8y^2=x\left(x+2y\right)-4y\left(x+2y\right)=\left(x+2y\right)\left(x-4y\right)\)
\(10x\left(x-y\right)-6y\left(y-x\right)\)
\(=10x\left(x-y\right)+6x\left(x-y\right)\)
\(=\left(10x+6x\right)\left(x-y\right)\)
\(c,3x^2+5y-3xy-5x\)
\(=\left(3x^2-3xy\right)+\left(5y-5x\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(3x-5\right)\left(x-y\right)\)
\(e,27+27x+9x^2=3\left(9+9x+x^2\right)\)
\(\left(x-1\right)^2-25\)
\(=x^2-2x+1-25\)
\(=x^2-2x-24\)
\(=x^2-6x+4x-24\)
\(=x.\left(x-6\right)+4.\left(x-6\right)\)
\(=\left(x+4\right).\left(x-6\right)\)
a, \(1-2y+y^2=\left(y+1\right)^2=\left(y+1\right)\left(y+1\right)\)
b, \(\left(x+1\right)^2-25=\left(x+1\right)^2-5^2=\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)
c, \(1-4x^2=1^2-\left(2x\right)^2=\left(1-2x\right)\left(1+2x\right)\)
d, \(8-27x^3=2^3-\left(3x\right)^3=\left(2-3x\right)\left(4+6x+9x^2\right)\)
a) \(x^3+8y^3+4x+8y\)
\(=x^3-2x^2y+4xy^2+4x+2x^2y-4xy^2+8y^3+8y\)
\(=\left(x^3-2x^2y+4xy^2+4x\right)+\left(2x^2y-4x^2y+8y^3+8y\right)\)
\(=x\left(x^2-2xy+4y^2+4\right)+2y\left(x^2-2xy+4y^2+4\right)\)
\(=\left(x^2-2xy+4y^2+4\right)\left(x+2y\right)\)
b) \(x^2+6xy+9y^2+5x+15y\)
\(=\left(x^2+6xy+9y^2\right)+\left(5x+15y\right)\)
\(=\left(x+3y\right)^2+5\left(x+3y\right)\)
\(=\left(x+3y\right)\left(x+3y+5\right)\)
c) \(25-x^2+2xy-y^2\)
\(=25-\left(x^2-2xy+y^2\right)\)
\(=25-\left(x-y\right)^2\)
\(=5^2-\left(x-y\right)^2\)
\(=\left(5+x-y\right)\left(5-x+y\right)\)
`x^3+8y^3 +4x+8y`
`=(x+2y)(x^2 - 2xy + 4y^2 ) +4 (x+2y)`
`= (x+2y) (x^2 -2xy +4y^2 +4)`
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`x^2 +6xy +9y^2 +5x+15y`
`= (x+3y)^2 + 5(x+3y)`
`=(x+3y)( x+3y +5)`
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`25-x^2 +2xy -y^2`
`= 25 - (x^2 -2xy+y^2)`
`=25-(x-y)^2`
`=(5-x+y)(5+x-y)`