Toán Lớp 8: Phân tích đa thức thành nhân tử 1.27xy-18x²y+3x³y 2.2x³-8 3.9x²-(x-1)² 4.x²-3x+6y-4y² 5.x²-2(x-3)²-9 6.x⁴-2x³-x+2 7.x²-2x-8

Question

Toán Lớp 8:  Phân tích đa thức thành nhân tử 1.27xy-18x²y+3x³y 2.2x³-8 3.9x²-(x-1)² 4.x²-3x+6y-4y² 5.x²-2(x-3)²-9 6.x⁴-2x³-x+2 7.x²-2x-8

ngocbichchau · Answer

$1)$   $27xy-18x^2y+3x^3y$   $=3xy left(9-6x+x^2 right)$   $=3xy left(x-3 right) left(x-3 right)$   $=3xy left(x-3 right)^2$   $2)$   $2x^3-8$   $=2x^3-2 cdot  :4$   $=2 left(x^3-4 right)$   $3)$   $9x^2- left(x-1 right)^2$   $=9x^2-x^2+2x-1$   $=8x^2+2x-1$   $4)$   $x^2-3x+6y-4y^2$   $= left(x+2y right) left(x-2y right)+3 left(-x+2y right)$   $= left(x+2y right) left(x-2y right)-3 left(x-2y right)$   $= left(x-2y right) left(x+2y-3 right)$   $5)$   $x^2-2 left(x-3 right)^2-9$   $=x^2-2x^2+12x-18-9$   $=x^2-2x^2+12x-27$   $=-x^2+12x-27$   $6)$   $x^4-2x^3-x+2$   $= left(x^4-2x^3 right)+ left(-x+2 right)$   $=x^3 left(x-2 right)- left(x-2 right)$   $= left(x-2 right) left(x^3-1 right)$   $= left(x-2 right) left(x-1 right) left(x^2+x+1 right)$   $7)$   $x^2-2x-8$   $= left(x^2+2x right)+ left(-4x-8 right)$   $=x left(x+2 right)-4 left(x+2 right)$   $= left(x+2 right) left(x-4 right)$