Phân tích các đa thức sau thành nhân tử:
a) (3x-1)^2 – 16
b) (5x-4)^2 -49x²
d) (3x +1)^2– 4(x – 2)^2
g) (ax + by)^2 – (ay + bx)²
i) (4x² – 3x – 18)² – (4x² +3x)²
I) -4^2 +12xy –9y² +25
c) (2x +5)^2 -(x-9) ²
Phân tích các đa thức sau thành nhân tử: a) (3x-1)^2 – 16 b) (5x-4)^2 -49x² d) (3x +1)^2– 4(x – 2)^2 g) (ax + by)^2 – (ay + bx)² i) (4x² – 3x – 18)² –
By Audrey
a, (3x-1)²-16
= (3x-1)²-4²
= (3x-1-4)(3x-1+4)
= (3x-5)(3x+3)
b, (5x-4)²-49x²
= (5x-4)²-(7x)²
= (5x-4-7x)(5x-4+7x)
=(-2x-4)(12x-4)
d, (3x+1)²-4(x-2)²
= (3x+1)²-[2(x-2)]²
= [3x+1-2(x-2)][3x+1+2(x-2)]
= (3x+1-2x+4)(3x+1+2x-4)
= (x+5)(5x-3)
g, (ax+by)²-(ay+bx)²
= (ax+by-ay-bx)(ax+by+ay+bx)
i, (4x²-3x-18)²-(4x²+3x)²
= (4x²-3x-18-4x²-3x)(4x²-3x-18+4x²+3x)
= (-6x-18)(8x²-18)
l, 4x²+12xy-9y²-25
= (4x²-12xy+9y²)-25
= (2x-3y)²-5²
= (2x-3y-5)(2x-3y+5)
c, (2x+5)²-(x-9)²
= (2x+5-x+9)(2x+5+x-9)
= (x+14)(3x-4)
`a, (3x-1)²-16`
`= (3x-1)²-4²`
`= (3x-5)(3x+3)`
`b, (5x-4)²-49x²`
`= (5x-4)²-(7x)²`
`=(-2x-4)(12x-4)`
`d, (3x+1)²-4(x-2)²`
`= (3x+1)²-[2(x-2)]²`
`= [3x+1-2(x-2)][3x+1+2(x-2)]`
`= (x+5)(5x-3)`
`g, (ax+by)²-(ay+bx)²`
`= (ax+by-ay-bx)(ax+by+ay+bx)`
`i, (4x²-3x-18)²-(4x²+3x)²`
`= (4x²-3x-18-4x²-3x)(4x²-3x-18+4x²+3x)`
`= (-6x-18)(8x²-18)`
`l, 4x²+12xy-9y²-25`
`= (4x²-12xy+9y²)-25`
`= (2x-3y)²-5²`
`= (2x-3y-5)(2x-3y+5)`
`c, (2x+5)²-(x-9)²`
`= (x+14)(3x-4)`
Xin hay nhất !