Question

các cậu ơi giúp mik vs ạ
Bài 1:Rút gọn
a)\(\left(x-2\right)\)x\(\left(x^2+2x+4\right)\)-\(6x^2+12x\)
b)\(\left(2x+5\right)\)x\(\left(5-2x\right)+\left(x-5\right)\)x\(\left(5+4x\right)\)
c)\(4x^2+4x+1-\left(2x-1\right)^2\)
d)\(\left(x+5\right)\)x\(\left(x^2+5x+25\right)-10x\) x\(\left(x+5\right)-x^3\)

Answer 1

a: \(=x^3-8-6x^2+12x=\left(x-2\right)^3\)

b: \(=25-4x^2+5x+4x^2-25-20x=-15x\)

c: \(=4x^2+4x+1-4x^2+4x-1=8x\)

d: \(=x^3+125-10x^2-50x-x^3=-10x^2-50x+125\)

Answer 2

Lời giải:

a.

$(x-2)(x^2+2x+4)-6x^2+12=(x-2)(x^2+2x+4)-6x(x-2)$

$=(x-2)(x^2+2x+4-6x)=(x-2)(x^2-4x+4)=(x-2)(x-2)^2=(x-2)^3$

b.

$(2x+5)(5-2x)+(x-5)(5+4x)=-(2x+5)(2x-5)+(4x+5)(x-5)$

$=-(4x^2-25)+(4x^2-15x-25)$

$=-4x^2+25+4x^2-15x-25=4x^2$

c.

$4x^2+4x+1-(2x-1)^2=(2x+1)^2-(2x-1)^2=(2x+1-2x+1)(2x+1+2x-1)$

$=2.4x=8x$

d.

$(x+5)(x^2+5x+25)-10x(x+5)-x^3$

$=(x+5)(x^2+5x+25-10x)-x^3$
$=(x+5)(x^2-5x+25)-x^3$

$=x^3+5^3-x^3=125$