1D  2C

Câu 1: D

Câu 2: C

a) xy+3x-7y-21

=x(y+3)-7(x+3)

=(x-7)(y+3)

b)2xy-15-6x-5y

=2x(y-3)-5(-3+y)

=(2x-5)(y-3)

c)2x^2y+2xy^2-2x-2y

=2x(xy-1)+2y(xy-1)

=(2x+2y)(xy-1)

x(x+3)-5x(x-5)-5(x+3)

=(x-5)(x+3)-5x(x-5)

=(x-5)(x+3-5x)

Câu cuối mình bị nhầm dòng cuối phải là (x-5)(x+3+x-5)=(x-5)(2x-2)nha bạn

a) xy+3x-7y-21=(xy+3x)-(7y+21)= x(y+3)-7(y+3)=(y+3)(x-7)

b)2xy-15-6x+5y=(2xy-6x)+(5y-15)=2x(y-3)+5(y-3)=(y-3)(2x+5)

c)2x^2y+2xy^2-2x-2y=2xy(x+y)-2(x+y)=2(x+y)(xy-1)

d) x(x+3)-5x(x-5)-5(x+3)=[x(x+3)-5(x+3)]-5x(x-5)=(x+3)(x-5)-5x(x-5)=(x-5)(x+3-5x)=(x-5)(3-4x)

a) \(x^3y^3+x^2y^2+4\)

\(=x^3y^3-x^2y^2+2x^2y^2-2xy+2xy+4\)

\(=\left(x^3y^3-x^2y^2+2xy\right)+\left(2x^2y^2-2xy+4\right)\)

\(=xy\left(x^2y^2-xy+2\right)+2\left(x^2y^2-xy+2\right)\)

\(=\left(xy+2\right)\left(x^2y^2-xy+2\right)\)

b) \(x^3+3x^2y-9xy^2+5y^3\)

\(=x^3+5x^2y-2x^2y-10xy^2+xy^2+5y^3\)

\(=\left(5y^3-10xy^2+5x^2y\right)+\left(xy^2-2x^2y+x^3\right)\)

\(=5y\left(y^2-2xy+x^2\right)+x\left(y^2-2xy+x^2\right)\)

\(=\left(5y+x\right)\left(y^2-2xy+x^2\right)\)

\(=\left(5y+x\right)\left(y-x\right)^2\)

\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

1.

$4x^2y+5x^3-x^2y^2=x^2(4y+5x-y^2)$

2.

$5x(x-1)-3y(1-x)=5x(x-1)+3y(x-1)=(x-1)(5x+3y)$

3.

$4x^2-25=(2x)^2-5^2=(2x-5)(2x+5)$

4.

$6x-9-x^2=-(x^2-6x+9)=-(x-3)^2$

5.

$x^2+4y^2+4xy=x^2+2.x.2y+(2y)^2=(x+2y)^2$

6.

$\frac{1}{64}-27x^3=(\frac{1}{4})^3-(3x)^3$
$=(\frac{1}{4}-3x)(\frac{1}{16}+\frac{3x}{4}+9x^2)$
 

7.

$x^3-6x^2+12x-8=x^3-3.x^2.2+3.x.2^2-2^3$

$=(x-2)^3$
8.

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

$=(x+y)(x-y-1)$

9.

$5x-5y+ax-ay=5(x-y)+a(x-y)$

$=(x-y)(5+a)$

\(1,=\left(x-3\right)\left(x+3\right)\\ 2,=\left(x-y\right)\left(5+a\right)\\ 3,=\left(x+3\right)^2\\ 4,=\left(x-y\right)\left(10x+7y\right)\\ 5,=5\left(x-3y\right)\\ 6,=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)

bạn gõ lại công thức cho rõ đi, khó đọc quá

Ta có 3x(x – 3y) + 9y(3y – x)

= 3x(x – 3y) – 9y(x – 3y) = (x – 3y)(3x – 9y)

= (x – 3y).3(x – 3y) = 3 ( x   –   3 y ) 2

Đáp án cần chọn là: A

a)

\(10x^2+10xy+5x+5y\)

\(=10x\left(x+y\right)+5\left(x+y\right)\)

\(=5\left(x+y\right)\left(2x+1\right)\)

b)

\(x^3+x^2-x-1\)

\(=x^2\left(x+1\right)-\left(x+1\right)\)

\(=\left(x-1\right)\left(x^2-1\right)\)

\(=\left(x-1\right)^2\left(x+1\right)\)

c)

\(x+2a\left(x-y\right)-y\)

\(=\left(x-y\right)+2a\left(x-y\right)\)

\(=\left(x-y\right)\left(2a+1\right)\)

d)

\(x^2-y^2+7x-7y\)

\(=\left(x+y\right)\left(x-y\right)+\left(x-y\right)\)

\(=\left(x-y\right)\left(x+y+1\right)\)

\(4x\left(x-y\right)+7y\left(x-y\right)+y^2\left(y-x\right)=\left(y-x\right)\left(y^2-7y-4x\right)\)

4x( y - x ) + 7y( x - y ) + y²( y - x )

= 4x( y - x ) - 7y( y - x ) + y²( y - x )

= ( y - x )( 4x - 7y + y² )