Câu hỏi của Trần Thị Hảo

Question

NHÓM HẠNG TỬ - PHỐI HỢP
a) x2 (y - z) + y2 (z - x) + z2 (x - y)
b) (x - y)3 - x3 - y3
c) (x + y + z)3 -x3 - y3 - z3
d) (x2 + y2 - 5)2 - 4x2y2 - 16xy -16
e) (x2 + 4y2 - 5)2 - 16(x2y2 + 2xy +1)
f) (x -...

Phong Thần · Accepted Answer

a) $x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)$

$=x^2\left(y-z\right)-y^2\left[\left(y-z\right)+\left(x-y\right)\right]+z^2\left(x-y\right)$

$=x^2\left(y-z\right)-y^2\left(y-z\right)-y^2\left(x-y\right)+z^2\left(x-y\right)$

$=\left(y-z\right)\left(x^2-y^2\right)-\left(x-y\right)\left(y^2-z^2\right)$

$=\left(y-z\right)\left(x-y\right)\left(x+y\right)-\left(x-y\right)\left(y-z\right)\left(y+z\right)$

$=\left(x-y\right)\left(y-z\right)\left(x+y-y-z\right)$

$=\left(x-y\right)\left(y-z\right)\left(x-z\right)$Câu trả lời: a) $x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)$

$=x^2\left(y-z\right)-y^2\left[\left(y-z\right)+\left(x-y\right)\right]+z^2\left(x-y\right)$

$=x^2\left(y-z\right)-y^2\left(y-z\right)-y^2\left(x-y\right)+z^2\left(x-y\right)$

$=\left(y-z\right)\left(x^2-y^2\right)-\left(x-y\right)\left(y^2-z^2\right)$

$=\left(y-z\right)\left(x-y\right)\left(x+y\right)-\left(x-y\right)\left(y-z\right)\left(y+z\right)$

$=\left(x-y\right)\left(y-z\right)\left(x+y-y-z\right)$

$=\left(x-y\right)\left(y-z\right)\left(x-z\right)$

Phong Thần · Answer

c) $\left(x+y+z\right)^3-x^3-y^3-z^3$

$=\left[\left(x+y\right)+z\right]^3-x^3-y^3-z^3$

$=\left(x+y\right)^3+z^3+3z\left(x+y\right)\left(x+y+z\right)-x^3-y^3-z^3$

$=\left[\left(x+y\right)^3-x^3-y^3\right]+3z\left(x+y\right)\left(x+y+z\right)$

$=3xy\left(x+y\right)+3\left(x+y\right)\left(xz+yz+z^2\right)$

$=3\left(x+y\right)\left(xy+xz+yz+z^2\right)$

$=3\left(x+y\right)\left[x\left(y+z\right)+z\left(y+z\right)\right]$

$=3\left(x+y\right)\left(y+z\right)\left(x+z\right)$

d) $\left(x^2+y^2-5\right)^2-4x^2y^2-16xy-16$

$=\left(x^2+y^2-5\right)^2-\left(4x^2y^2+16xy+16\right)$

$=\left(x^2+y^2-5\right)^2-\left[\left(2xy\right)^2+2.2xy.4+16\right]$

$=\left(x^2+y^2-5\right)^2-\left(2xy+4\right)^2$

$=\left(x^2+y^2-5-2xy-4\right)\left(x^2+y^2-5+2xy+4\right)$

$=\left(x^2-2xy+y^2-9\right)\left(x^2+2xy+y^2-1\right)$

$=\left[\left(x-y\right)^2-3^2\right]\left[\left(x+y\right)^2-1\right]$

$=\left(x-y-3\right)\left(x-y+3\right)\left(x+y-1\right)\left(x+y+1\right)$

e) $\left(x^2+4y^2-5\right)^2-16\left(x^2y^2+2xy+1\right)$

$=\left(x^2+4y^2-5\right)^2-4^2\left(xy+1\right)^2$

$=\left(x^2+4y^2-5\right)^2-\left[4\left(xy+1\right)\right]^2$

$=\left(x^2+4y^2-5\right)-\left(4xy+4\right)^2$

$=\left(x^2+4y^2-5-4xy-4\right)\left(x^2+4y^2-5+4xy+4\right)$

$=\left(x^2+4y^2-4xy-9\right)\left(x^2+4y^2+4xy-1\right)$

$=\left[\left(x-2y\right)^2-3^2\right]\left[\left(x+2y\right)^2-1\right]$

$=\left(x-2y-3\right)\left(x-2y+3\right)\left(x+2y-1\right)\left(x+2y+1\right)$

f) $\left(x-y+5\right)^2-2\left(x-y+5\right)+1$

$=\left(x-y+5-1\right)^2$

$=\left(x-y+4\right)^2$Câu trả lời: c) $\left(x+y+z\right)^3-x^3-y^3-z^3$