Question

Answer 1

2. 

$(2x^2+x-1)(x+2)=2x^3+4x^2+x^2+2x-x-2$

$=2x^3+5x^2+x-2$
3.

$(x-y)(x^2+xy+y^2)=x^3-y^3$ (hđt quen thuộc)

4.

$(x+1)(x^2-1)=x^3-x+x^2-1=x^3+x^2-x-1$

 

Answer 2

5.

$(x+2)(x^2-2x+4)=x^3+2^3=x^3+8$

6.

$(x-2y)(x^2+2xy+4y^2)=x^3-(2y)^3=x^3-8y^3$
7.

$3x(x-2)(x+2)=3x(x^2-4)=3x^3-12x$

8.

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

$=(4x^2)^2-1=16x^4-1$

 

Answer 3

9.

$4(x^2-\frac{y}{2})(x^2+\frac{y}{2})$

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

10.

$(x+y)(x^2-xy+y^2)=x^3+y^3$

11.

$(x^2-2xy+y^2)(x-y)=(x-y)^2(x-y)=(x-y)^3$
$=x^3-3x^2y+3xy^2-y^3$
12.

$(2x-y)(4x^2+2xy+y^2)(8x^3+y^3)$

$=[(2x)^3-y^3](8y^3+y^3)=(8x^3-y^3)(8x^3+y^3)$

$=(8x^3)^2-(y^3)^2=64x^6-y^6$

Answer 4

13.
$(x-1)(x+1)(x^2-x+3)=(x^2-1)(x^2-x+3)$

$=x^4-x^3+3x^2-x^2+x-3$

$=x^4-x^3+2x^2+x-3$

14.

$\frac{1}{2}x^2y^2(2x+y)(2x-y)$

$=\frac{1}{2}x^2y^2(4x^2-y^2)$
$=\frac{1}{2}(4x^4y^2-x^2y^4)$

$=2x^4y^2-\frac{1}{2}x^2y^4$

15.

$(a-x)(a+x)(a^2+x^2)=(a^2-x^2)(a^2+x^2)$

$=a^4-x^4$

16.

$(2a-1)(3a+2)(3-a)$

$=(2a-1)(9a-3a^2+6-2a)$

$=(2a-1)(-3a^2+7a+6)$

$=-6a^3+14a^2+12a+3a^2-7a-6$

$=-6a^3+17a^2+5a-6$