\(B=\frac{5x^2-10y}{2.\left(2y-x^2\right)}\)

\(B=\frac{5.\left(x^2-2y\right)}{2.\left(2y-x^2\right)}\)

\(B=\frac{-5.\left(2y-x^2\right)}{2.\left(2y-x^2\right)}\)

\(B=\frac{-5}{2}.\)

Mình nghĩ là \(x^2\) thì đúng hơn.

Chúc bạn học tốt!

Lời giải:
$\frac{x}{y}$ không phải đơn thức bạn nhé.

a. $x^2-2x+1=(x-1)^2$

b. $x^2+2xy-25+y^2=(x^2+2xy+y^2)-25=(x+y)^2-5^2=(x+y-5)(x+y+5)$

c. $5x^2-10xy=5x(x-2y)$

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

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

giải hết nha đừng có ghi kết quả

Bài 1 :

a,\(x\left(x+y\right)-6x-6y=x\left(x+y\right)-6\left(x+y\right)=\left(x+y\right)\left(x-6\right)\)

b, \(x^3-x-y^2-y??????????\)

c, \(2x^3+16=2\left(x^3+8\right)=2\left(x+3\right)\left(x^2-3x+9\right)\)

d, \(x^4+2x^3+x^2=x^2\left(x^2+2x+1\right)=x^2\left(x+1\right)^2\)

e, \(5x^2-10xy+5y^2-20z^2=5[\left(x-y\right)^2-\left(2z\right)^2]\)

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

f, \(16-x^2+2xy-y^2=16-\left(x-y\right)^2=\left(4-x+y\right)\left(4+x-y\right)\)

g, Tương tự e

Bài 2 :

a,\(x^2-10x=-25< =>\left(x-5\right)^2=0< =>x=5\)

b,\(x^2\left(x-2\right)+x-2=0\)

\(\Leftrightarrow\left(x-2\right)\left(x^2+1\right)=0\)

\(x^2+1>0< =>x-2=0< =>x=2\)

c, \(\left(x-2\right)^2=\left(3x-5\right)^2\)

\(< =>\left[{}\begin{matrix}x-2=3x-5\\x-2=5x-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1,5\\x=0,25\end{matrix}\right.\)

\(1,=6xy\left(x^2-2xy+y^2\right)=6xy\left(x-y\right)^2\\ 2,=\left(x^2+4-4\right)\left(x^2+4+4\right)=x^2\left(x^2+8\right)\\ 3,=5x\left(x-y\right)-10\left(x-y\right)=5\left(x-2\right)\left(x-y\right)\\ 4,=\left(a-b\right)\left(a^2+ab+b^2\right)-3\left(a-b\right)=\left(a-b\right)\left(a^2+ab+b^2-3\right)\\ 5,=\left(x-1\right)^2-y^2=\left(x+y-1\right)\left(x-y-1\right)\\ 6,Sửa:x^2-x-2=x^2+x-2x-2=\left(x+1\right)\left(x-2\right)\\ 7,=x^4-4x^2-x^2+4=\left(x^2-4\right)\left(x^2-1\right)\\ =\left(x-2\right)\left(x+2\right)\left(x-1\right)\left(x+1\right)\\ 8,=-x^3-x^2-x=-x\left(x^2+x+1\right)\\ 9,=\left(a-3\right)\left(a^2+3a+9\right)+\left(a-3\right)\left(6a+9\right)\\ =\left(a-3\right)\left(a^2+9a+18\right)\\ =\left(a-3\right)\left(a^2+3a+6a+18\right)\\ =\left(a-3\right)\left(a+3\right)\left(a+6\right)\)

\(10,=x^2y-x^2z+y^2z-xy^2+z^2\left(x-y\right)\\ =xy\left(x-y\right)-z\left(x-y\right)\left(x+y\right)+z^2\left(x-y\right)\\ =\left(x-y\right)\left(xy-xz-yz+z^2\right)\\ =\left(x-y\right)\left(x-z\right)\left(y-z\right)\)

a) (a - 2b)x(a + 2b)
b) x²-(y-3)²
 => (x-y+3)(x+y-3)
c) (2a + b - a)(2a + b + a)
=> (a+b)(3a+b)
d) (4(x - 1))² - (5(x + y))²
⇔ (4x - 4 - 5x - 5y)(4x - 4 + 5x + 5y)
⇔ -(x + 5y + 4)(9x + 5y + -4)
e) (x + 5)²
f) (5x - 2y)²
h) (x - 5)(x² + 5x + 25)

k) (x + 5)³

d: \(x\left(x^2-1\right)+3\left(x^2-1\right)\)

\(=\left(x-1\right)\left(x+1\right)\left(x+3\right)\)

e: \(x^2-10x+25=\left(x-5\right)^2\)

g: \(x^2-64=\left(x-8\right)\left(x+8\right)\)

h: \(\left(x+y\right)^2-\left(x^2-y^2\right)\)

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

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

i: \(5x^2+5xy-x-y\)

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

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

k: \(x^2+2xy+y^2-25=\left(x+y-5\right)\left(x+y+5\right)\)

l: \(2xy-x^2-y^2+16\)

\(=-\left(x^2-2xy+y^2-16\right)\)

\(=-\left(x-y-4\right)\left(x-y+4\right)\)

a: \(5x-15y=5\left(x-3y\right)\)

b: \(5x^2y^2+15x^2y+30xy^2=5xy\left(xy+3x+6y\right)\)

c: \(x^3-2x^2y+xy^2-9x\)

\(=x\left(x^2-9-2xy+y^2\right)\)

\(=x\left(x-y-3\right)\left(x-y+3\right)\)

Câu 1: A

Câu 21: A

\(16,A\\ 17,C\\ 18,A\\ 19,C\\ 20,A\\ 21,A\)

1a

1) c) 25-x²+2xy-y²

=5²-(x²-2xy+y²)

=5²-(x-y)²

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

d) 2x²+7x+5

= 2x²+2x+5x+5

=2x(x+1)+5(x+1)

=(2x+5)(x+1)

e) x³-3x²-4x+12

=x²(x-3)-4(x-3)

=(x²-4)(x-3)

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

g) 5x³-5x²y-10x²+10xy

=5x²(x-y)-10x(x-y)

=(5x²-10x)(x-y)

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