Question

Phân tích các đa thức sau thành nhân tử :

a) 4x²-1

b) 25a²-0,01

c) 2a(x+y)-3b(x+y)

d) 4x²-12xy+9y²

g) (x+y)²-2(x+y)+1

h) x⁴-9x³+x²-9x

i) x²-x-y²-y

k) a³-a²x+ax+xy

Answer 1

a) \(4x^2-1=\left(2x\right)^2-1^2=\left(2x-1\right)\left(2x+1\right)\)

b) \(25a^2-0.01=\left(5a\right)^2-\left(0.1\right)^2=\left(5a-0.1\right)\left(5a+0.1\right)\)

Answer 2

a, \(4x^2-1\)

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

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

b,\(25a^2-0,01\)

=\(\left(5a\right)^2-\left(0,1\right)^2\)

=\(\left(5a-0,1\right)\left(5a+0,1\right)\)

c,2a(x+y)-3b(x+y)

=(x+y)(2a-3b)

d,\(4x^2-12xy+9y^2\)

=\(\left(2x-3y\right)^2\)

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

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

h,\(x^4-9x^3+x^2-9x\)

=\(x^3\left(x-9\right)+x\left(x-9\right)\)

=\(\left(x^3+x\right).\left(x-9\right)\)

=\(x.\left(x^2+1\right).\left(x-9\right)\)

i,\(x^2-x-y^2-y\)

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

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

=\(\left(x+y\right).\left(x-y-1\right)\)

Answer 3

c. 2a(x+y)-3b(x+y)=(x+y)(2a-3b)

d. \(4x^2-12xy+9y^2=\left(2x\right)^2-2.2x.3y+\left(3y\right)^2=\left(2x-3y\right)^2\)

Answer 4

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

h. \(x^4-9x^3+x^2-9x=x^3\left(x-9\right)+x\left(x-9\right)=\left(x-9\right)\left(x^3+x\right)=x\left(x-9\right)\left(x^2+1\right)\)