Phân tích đa thức thành nhân tử :
4(x2y2 + z2t2 + 2xyzt) - (x2 + y2 - z2 - t2)2
Nhớ là phân tích triệt để cho mik nha !!!!!
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DN
4
TA
1 tháng 9 2021
`16x^2z^2+y^2-z^2-16x^2y^2`
`=16x^2(z^2-y^2)+(y^2-z^2)`
`=16x^2(z-y)(y+z)+(y-z)(y+z)`
`=(y+z)[16x^2(z-y)+y-z]`
`=(y+z)(16x^2z-16x^2y+y-z)`
1 tháng 9 2021
a: Ta có: \(a^5-ax^4+a^4x-x^5\)
\(=a\left(a^4-x^4\right)+x\left(a^4-x^4\right)\)
\(=\left(a-x\right)\left(a+x\right)\left(a^2+x^2\right)\cdot\left(a+x\right)\)
\(=\left(a-x\right)\cdot\left(a+x\right)^2\cdot\left(a^2+x^2\right)\)
DN
2
4 tháng 9 2021
x2-2xy+y2+3x-3y-10
= (x-y)2+3(x-y)-10
= [(x-y)2+5(x-y)]-[2(x-y)+10]
= (x-y)(x-y+5)-2(x-y+5)
= (x-y+5)(x-y-2)
4 tháng 9 2021
Ta có: \(x^2-2xy+y^2+3x-3y-10\)
\(=\left(x-y\right)^2+3\left(x-y\right)-10\)
\(=\left(x-y+5\right)\left(x-y-2\right)\)
DN
2
31 tháng 8 2021
\(4\left(x^2y^2+z^2t^2+2xyzt\right)-\left(x^2+y^2-z^2-t^2\right)^2\)
\(=\left[2\left(xy+zt\right)\right]^2-\left(x^2+y^2-z^2-t^2\right)^2\)
\(=\left(2xy+2zt\right)^2-\left(x^2+y^2-z^2-t^2\right)^2\)
\(=\left(2xy+2zt-x^2-y^2+z^2+t^2\right)\left(2xy+2zt+x^2+y^2-z^2-t^2\right)^2\)
31 tháng 8 2021
Ta có: \(4\left(x^2y^2+2xyzt+z^2t^2\right)-\left(x^2+y^2-z^2-t^2\right)^2\)
\(=\left(2xy+2tz\right)^2-\left(x^2+y^2-z^2-t^2\right)^2\)
\(=\left(2xy+2tz-x^2-y^2+z^2+t^2\right)\left(2xy+2tz+x^2+y^2-z^2-t^2\right)\)
\(=\left[-\left(x^2-2xy+y^2\right)+\left(z^2+2tz+t^2\right)\right]\left[\left(x^2+2xy+y^2\right)-\left(t^2-2tz+z^2\right)\right]\)
\(=\left(z+t-x+y\right)\left(z+t+x-y\right)\left(x+y-t+z\right)\left(x+y+t-z\right)\)
12 tháng 9 2021
\(4(x^2y^2+z^2t^2+2xyzt)-(x^2+y^2-z^2-t^2)^2\)
\(=[2(xy+zt]^2-(x^2+y^2-z^2-t^2)^2\)
\(=(2xy+2zt)^2-(x^2+y^2-z^2-t^2)^2\)
\(=(2xy+2zt-x^2-y^2+z^2+t^2)(2xy+2zt+x^2+y^2-z^2-t^2)^2\)
DN
3
4 tháng 9 2021
\(4\left(x^2+15x+50\right)\left(x^2+18x+72\right)-3x^2\\ =4\left(x+5\right)\left(x+10\right)\left(x+6\right)\left(x+12\right)-3x^2\\ =4\left(x^2+16x+60\right)\left(x^2+17x+60\right)-3x^2\)
Đặt \(x^2+16x+60=a\)
\(=4a\left(a+x\right)-3x^2\\ =4a^2+4ax-3x^2\\ =\left(2a-x\right)\left(2a+3x\right)\\ =\left[2\left(x^2+16x+60\right)-x\right]\left[2\left(x^2+16x+60\right)+3x\right]\\ =\left(2x^2+31x+120\right)\left(2x^2+35x+120\right)\)
BK
12 tháng 5 2023
(x2+15x+50)(x2+18x+72)−3x2=4(x+5)(x+10)(x+6)(x+12)−3x2=4(x2+16x+60)(x2+17x+60)−3x24(�2+15�+50)(�2+18�+72)−3�2=4(�+5)(�+10)(�+6)(�+12)−3�2=4(�2+16�+60)(�2+17�+60)−3�2
Đặt x2+16x+60=a�2+16�+60=�
=4a(a+x)−3x2=4a2+4ax−3x2=(2a−x)(2a+3x)=[2(x2+16x+60)−x][2(x2+16x+60)+3x]=(2x2+31x+120)(2x2+35x+120)
DN
4
1 tháng 9 2021
\(x^2\left(x+4\right)^2-\left(x+4\right)^2-\left(x^2-1\right)\\ =\left(x+4\right)^2\left(x^2-1\right)-\left(x^2-1\right)\\ =\left(x^2-1\right)\left[\left(x+4\right)^2-1\right]\\ =\left(x-1\right)\left(x+1\right)\left(x+4-1\right)\left(x+4+1\right)\\ =\left(x-1\right)\left(x+1\right)\left(x+3\right)\left(x+5\right)\)
2 tháng 9 2021
\(x^2-2x-24\\ =x^2-2x+1-25\\ =\left(x-1\right)^2-5^2\\ =\left(x-1-5\right)\left(x-1+5\right)\\ =\left(x-6\right)\left(x+4\right)\)
\(4\left(x^2y^2+z^2t^2+2xyzt\right)-\left(x^2+y^2-z^2-t^2\right)^2\)
\(=\left(2xy-2tz\right)^2-\left(x^2+y^2-z^2-t^2\right)\)
\(=\left(2xy-2tz-x^2-y^2+z^2+t^2\right)\left(2xy-2tz+x^2+y^2-z^2-t^2\right)\)
\(=\left[-\left(x-y\right)^2+\left(z-t\right)^2\right]\left[\left(x+y\right)^2-\left(t+z\right)^2\right]\)
\(=-\left(x-y-z+t\right)\left(x-y+z-t\right)\left(x+y-t-z\right)\left(x+y+t+z\right)\)
4(x2y2+z2t2+2xyzt)−(x2+y2−z2−t2)24(x2y2+z2t2+2xyzt)−(x2+y2−z2−t2)2
=[2(xy+zt)]2−(x2+y2−z2−t2)2=[2(xy+zt)]2−(x2+y2−z2−t2)2
=(2xy+2zt)2−(x2+y2−z2−t2)2=(2xy+2zt)2−(x2+y2−z2−t2)2
=(2xy+2zt−x2−y2+z2+t2)(2xy+2zt+x2+y2−z2−t2)2