Question

Câu 2: Phân tích các đa thức sau thành nhân tử :

a) (3x-1)^2-16

b) (5x-4)^2 -49x^2

c) (2x+5)^2 -(x-9)^2

d) (3x+1)^2 -4(x-2)^2

e) 9(2x+3)^2 -4(x+1)^2

f) 4b^2c^2-(b^2+c^2-a^2)^2

g) (ax+by)^2 - (ay+bx)^2

h) (a^2+b^2-5)^2 -4(ab+2)^2

i) (4x^2-3x-18)^2 -(4x^2+3x)^2

k) 9(x+y-1)^2 -4(2x+3y+1)^2

l) -4x^2 +12xy-9y^2+25

m) x^2-2xy+y^2-4m^2+4mn-n^2

Answer 1

\(a,\left(3x-1\right)^2-16=\left(3x-5\right)\left(3x+3\right)=3\left(x+1\right)\left(3x-5\right)\)

\(b,\left(5x-4\right)^2-49x^2=\left(12x-4\right)\left(-2x-4\right)=4\left(3x-1\right)\left(-2\right)\left(x+2\right)=-8\left(3x-1\right)\left(x+2\right)\)\(c,\left(2x+5\right)^2-\left(x-9\right)^2=\left(3x-4\right)\left(x+14\right)\)

Answer 2

a,\(\left(3x+1\right)^2-16=\left(3x-1-16\right)\left(3x-1+16\right)\\ =\left(3x-17\right)\left(3x+15\right)\)