Question

P/t đa thức thành nhân từ:

a, 10x (x - y) - 8 (y - x)

b, (3x + 1)^2 - (x + 1)^2

c, x^3 + y^3 + z^3 - 3xyz

Giúp mk a ~

Answer 1

a, 10x (x-y)-8(y-x)
=10x (x-y) +8(x-y)
=(10x+8) (x-y)
b,\(\left(3x+1\right)^2\)-\(\left(x+1\right)^2\)=\(\left(3x+1+x+1\right)\left(3x+1-x-1\right)\)
=(4x+2)2x
=4x(x+1)
c,\(x^3+y^3+z^3-3xyz=\left(x+y\right)^3-3xy\left(x+y\right)+z^3-3xyz\)
= \(\left[\left(x+y\right)^3+z^3\right]-3xy\left(x+y+z\right)\)
= \(\left(x+y+z\right)^3-3\left(x+y+z\right)\left(x+y\right)z-3xy\left(x+y+z\right)\)
=\(\left(x+y+z\right)^3-3\left(x+y+z\right)\left(xy+yz+zx\right)\)
= (x+y+z)\(\left[\left(x+y+z\right)^2-3xy-3yz-3zx\right]\)
= (x+y+z)\(\left(x^2+y^2+z^2-xy-yz-zx\right)\)

Answer 2

Phân tích đa thức thành nhân tử :

a) 10x. (x - y) - 8. (y - x)

= 10x. (x - y) + 8. (x - y)

= (x - y). (10x + 8)

b) (3x + 1)² - (x + 1)²

= (3x +1 - x - 1). (3x + 1 + x + 1)

= 2x. (4x + 2) = 4x. (2x + 1)

c) x³ + y³ + z³ - 3xyz

= (x + y + z). (x² + y² +z² - xy - yz - xz)

Chúc bạn học tốt !!!