thu gọn các biểu thức sau:
a,(12-2x).(8-3x)-6x(x-4)
b,(4x-1)(x+5)-(x-2)(x+3)
c,(3x+2)(x-1)-(x+4)(x-1/2)
d,(x+1)(1+x-x^2+x^3-x^4)-(x-1)(1+x+x^2+x^3+x^4)
thu gọn các biểu thức sau:
a,(12-2x).(8-3x)-6x(x-4)
b,(4x-1)(x+5)-(x-2)(x+3)
c,(3x+2)(x-1)-(x+4)(x-1/2)
d,(x+1)(1+x-x^2+x^3-x^4)-(x-1)(1+x+x^2+x^3+x^4)
Đáp án:
Giải thích các bước giải:
a/ $(12-2x)(8-3x)-6x(x-4)$
$=96-16x-36x+6x^2-6x^2+24x$
$=-28x+96$
b/ $(4x-1)(x+5)-(x-2)(x+3)$
$=4x^2-x+20x-5-x^2+2x-3x+6$
$=3x^2+18x+1$
c/ $(3x+2)(x-1)-(x+4)(x-\frac{1}{2})$
$=3x^2+2x-3x-2-x^2-4x+\frac{1}{2}x+2$
$=2x^2-\frac{9}{2}x$
d/ $(x+1)(1+x-x^2+x^3-x^4)-(x-1)(1+x+x^2+x^3+x^4)$
$=x+1+x^2+x-x^3-x^2+x^4+x^3-x^5-x^4-x+1-x^2+x-x^3+x^2-x^4+x^3-x^5+x^4$
$=-2x^5+2x+2=-2(x^5-x-1)$
Chúc bạn học tốt !!!
Bài làm
a) (12-2x).(8-3x)-6x(x-4)
= 96 – 16x – 36x + 6x² – 6x² + 24x
= 96 – 28x
b,(4x-1)(x+5)-(x-2)(x+3)
= 4x² + 20x – x – 5 – ( x² + 3x – 2x – 6 )
= 4x² + 20x – x – 5 – x² – 3x + 2x + 6
= 3x² – 18x + 1
c,(3x+2)(x-1)-(x+4)(x-1/2)
= 3x² – 3x + 2x – 2 – ( x² – 1/2x + 4x – 2 )
= 3x² – x – 2 – x² – 7/2x + 2
= 2x² – 9/2x
d,(x+1)(1+x-x²+x³-x⁴)-(x-1)(1+x+x²+x³+x⁴)
= x + x² – x³ + x⁴ – x⁵ + 1 + x – x² + x³ – x⁴ – ( x + x² + x³ + x⁴ + x⁵ – 1 – x – x² – x³ – x⁴ )
= 2x – x⁵ + 1 – ( x⁵ – 1 )
= 2x – x⁵ + 1 – x⁵ + 1
= 2x – 2x⁵ + 2