phân tích đa thức thành nhân tử:
a) (6x+3)-(2x-5)(2x+1)
b) (x-5)^2+(x+5)(x-5)-(5-x)(2x+1)
c) (3x-2)(4x-3)-(2-3x)(x-1)-2(3x-2)(x+1)
phân tích đa thức thành nhân tử:
a) (6x+3)-(2x-5)(2x+1)
b) (x-5)^2+(x+5)(x-5)-(5-x)(2x+1)
c) (3x-2)(4x-3)-(2-3x)(x-1)-2(3x-2)(x+1)
a) ( 6x + 3 ) – ( 2x – 5 ) ( 2x + 1 )
= 3. ( 2x + 1 ) – ( 2x – 5 ). ( 2x + 1 )
= ( 2x + 1 ) . ( 3 – 2x + 5 )
= ( 2x + 1 ) . ( 8 – 2x )
b) ( x-5 )² + ( x+5 ) ( x-5 ) – ( 5-x ) ( 2x+1 )
= x² − 10x + 25 + x² − 25 − 10x − 5 + 2x² + x
= 4x² − 19x − 5
= 4x² – 20x + x – 5
= 4x ( x – 5 ) + ( x – 5 )
= ( x – 5 ) ( 4x + 1 )
c) (3x-2) (4x-3) – (2-3x) (x-1) – 2 (3x-2) (x+1)
= (3x−2) (4x−3) + (3x−2) (x−1) – (3x−2) (2x+2)
= (3x−2) (4x- 3 + x – 1- 2x – 2)
= (3x−2) .(3x−6)
Đáp án:
a) (6x+3)-(2x-5)(2x+1)
=2x.3+3-(2x-5)(2x+1)
= 2x(3-1+1)+(3-5+1)
=2x(3-1+1)-1
b)
(x-5)²+(x+5)(x-5)-(5-x)(2x+1)
=x²-2.x.5+5²+x²-5x+5x-5²-10x-5-2x²-x
=(x²+x²-2x²)+(-10x-5x+5x-10x-x)+(5²-5²-5)
=-20x-5
=-5.4x-5
=-5(4x-1)
c)(3x-2)(4x-3)-(2-3x)(x-1)-2(3x-2)(x+1)
=12x²-9x-8x+6-2x-x-3x+3x-(6x+4)(x+1)
=12x²-9x-8x+6-2x-x-3x+3x-6x²-6x+4x+1
=(12x²-6x²)+(-9x-8x-2x-x-3x+3x-6x+4x)+(6+1)
=6x²-22x+7