Question

phân tích các đa thức sau thành nhân tử
a) 25.(x-2)^2 - 100.(y-3)^2
b) 4.(x+3)^2 - 9.(x+2)^2
c) x^2 - 10x - y^2 + 25
d) x^2 - 4x - y^2 + 4
e) (x^2 + 2)^2 - 2.(x^2 + 2) +1

Answer 1

a, \(25\left(x-2\right)^2-100\left(y-3\right)^2\)

\(=\left(5x-10\right)^2-\left(10y-30\right)^2\)

\(=\left(5x-10-10y+30\right)\left(5x-10+10y-30\right)\)

\(=\left(5x-10y+20\right)\left(5x+10y-40\right)\)

\(=25\left(x-2y+4\right)\left(x+2y-8\right)\)

b, \(4\left(x+3\right)^2-9\left(x+2\right)^2\)

\(=\left(2x+6\right)^2-\left(3x+6\right)^2\)

\(=\left(2x+6-3x-6\right)\left(2x+6+3x+6\right)\)

\(=-x\left(5x+12\right)\)

c, \(x^2-10x-y^2+25\)

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

\(=\left(x-y-5\right)\left(x+y-5\right)\)

d, \(x^2-4x-y^2+4\)

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

\(=\left(x-y-2\right)\left(x+y-2\right)\)

e, \(\left(x^2+2\right)^2-2\left(x^2+2\right)+1\)

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

\(=\left(x^2+1\right)^2\)