Phân tích các đa thức sau thành nhân tử
a) (3x -1)2 - 16
b) (5x - 4 )2 - 49x2
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) 4b2c2 - (b2 + c2 - a2)2
g) (ax + by)2 - ( ay + bx)2ư
h) (a2 + b2 - 5)2 - 4(ab + 2)2
i) (4x2 - 3x - 18)2 - ( 4x2 + 3x)2
k) 9( x + y - 1)2 -4(2x + 3y + 1)2
l) -4x2 + 12xy - 9y2 + 25
m) x2 - 2xy + y2 - 4m2 + 4mn - n2
Mike ko đủ thời gian nha😅x.lỗi
a) \(\left(3x-1\right)^2-4^2=\left(3x-1-4\right).\left(3x-1+4\right)\) \(=\left(3x-5\right).\left(3x+3\right)=\left(3x-5\right).3.\left(x+1\right)\)
b) \(\left(5x-4\right)^2-\left(7x\right)^2=\left(5x-4-7x\right).\left(5x-4+7x\right)\)
\(=\left(-2x-4\right).\left(12x-4\right)=\left(-2\right).\left(x-2\right).4.\left(3x-1\right)\)
\(=-8.\left(x-2\right).\left(3x-1\right)\)
c) \(\left(2x+5\right)^2-\left(x-9\right)^2=\left(2x+5-x+9\right).\left(2x+5+x-9\right)\)
\(=\left(x+14\right).\left(3x-4\right)\)
d) \(\left(3x+1\right)^2-2^2.\left(x-2\right)^2\) \(=\left(3x+1\right)^2-\left[2.\left(x-2\right)\right]^2\)
\(=\left[3x+1+2.\left(x-2\right)\right].\left[3x+1-2.\left(x-2\right)\right]\)
\(=\left(3x+1+2x-4\right).\left(3x+1-2x+4\right)\)
\(=\left(5x-3\right).\left(x+5\right)\)
e) \(\left[3.\left(2x+3\right)\right]^2-\left[2.\left(x+1\right)\right]^2\)
\(=\left(6x+9\right)^2-\left(2x+1\right)^2\)
\(=\left(6x+9-2x-1\right).\left(6x+9+2x+1\right)\)
\(=\left(4x+8\right).\left(8x+10\right)\) \(=4.\left(x+2\right).2.\left(4x+5\right)=8.\left(x+2\right).\left(4x+5\right)\)
f) \(\left(2bc\right)^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left(2bc-b^2-c^2+a^2\right).\left(2bc+b^2+c^2-a^2\right)\)
\(=-\left(b^2-2bc+c^2+a^2\right).\left(b^2+2bc+c^2-a^2\right)\)
\(=-\left[\left(b-c\right)^2+a^2\right].\left[\left(b+c\right)^2-a^2\right]\)