a) \(x^2-2x+1-y^2\)

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

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

b) \(x^2-8x+12\)

\(=x^2-8x+16-4\)

\(=\left(x-4\right)^2-2^2\)

\(=\left(x-4-2\right)\left(x-4+2\right)\)

\(=\left(x-6\right)\left(x-2\right)\)

a) x² - 2x + 1 - y²

= (x² - 2x + 1) - y²

= (x - 1)² - y²)

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

b) x² - 8x + 12

= x² - 6x - 2x + 12

= (x² - 6x) - (2x - 12)

= x(x - 6) - 2(x - 6)

= (x - 6)(x - 2)

a/

\(A=\dfrac{x+15}{\left(x-3\right)\left(x+3\right)}+\dfrac{2}{x+3}=\)

\(=\dfrac{x+15+2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{3x+9}{\left(x-3\right)\left(x+3\right)}=\dfrac{3}{x-3}\)

b/

\(\dfrac{3}{x-3}=-\dfrac{1}{2}\Rightarrow x=x=-3\)

c/

Để A nguyên

\(\Rightarrow x-3=\left\{-3;-1;1;3\right\}\)

\(\Rightarrow x=\left\{0;-2;4;6\right\}\)

`a,` \(\left\{{}\begin{matrix}x-2\ne0\Leftrightarrow x\ne2\\x+2\ne0\Leftrightarrow x\ne-2\end{matrix}\right.\)

\(b,A=\dfrac{x^2}{x^2-4}-\dfrac{x}{x-2}-\dfrac{2}{x+2}\\ =\dfrac{x^2}{\left(x-2\right)\left(x+2\right)}-\dfrac{x}{x-2}-\dfrac{2}{x+2}\\ =\dfrac{x^2-x\left(x+2\right)-2\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\\ =\dfrac{x^2-x^2-2x-2x+4}{\left(x-2\right)\left(x+2\right)}\\ =\dfrac{-4x+4}{x-4}\)

`c,` Để `A=2` ta có

 \(\dfrac{-4x+4}{x-4}=2\left(x\ne4\right)\\ \Leftrightarrow\dfrac{-4x+4}{x-4}=\dfrac{2\left(x-4\right)}{x-4}\\ \Leftrightarrow-4x+5=2x-8\\ \Leftrightarrow-6x=-13\\ \Leftrightarrow x=\dfrac{13}{6}\)

a) \(xy+y^2-x-y\)

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

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

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

b) \(\left(x^2y^2-8\right)^2-1\)

\(=\left(x^2y^2-8\right)^2-1^2\)

\(=\left(x^2y^2-8-1\right)\left(x^2y^2-8+1\right)\)

\(=\left(x^2y^2-9\right)\left(x^2y^2-7\right)\)

\(=\left(xy+3\right)\left(xy-3\right)\left(x^2y^2-7\right)\)

`a, xy +y^2 -x-y`

`=(xy+y^2)-(x+y)`

`= y(x+y)-(x+y)`

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

`b, (x^2y^2 -8)^2 -1`

`= (x^2y^2 -8)^2 -1^2`

`=(x^2y^2 -8-1)(x^2y^2-8+1)`

`=(x^2y^2 -9)(x^2y^2-7)`

a) Thể tích không khí bên trong chiếc lều:

1/3 . 3² . 2,8 = 8,4 (m³)

b) Diện tích đáy:

3.3 = 9 (m²)

Độ dài cạnh bên của lều:

√(2,8² + 1,5²) ≈ 3,18 (m)

Diện tích vải lều:

9 + 4 . 3 . 3,18 : 2 = 28,08 (m²)

Số tiền mua vải:

28,08 . 15000 - 28,08 . 15000 . 5% = 400140 (đồng)

Dcu bài như cc

a) Xét tứ giác ABCD ta có:

\(\widehat{A}+\widehat{B}+\widehat{C}+\widehat{D}=360^o\)

\(\Rightarrow\widehat{D}=360^o-102^o-102^o-102^o\)

\(\Rightarrow\widehat{D}=54^o\) 

b) Xét tam giác vuông AOD ta có:

\(AD^2=OD^2+OA^2\)

\(\Rightarrow OA=\sqrt{AD^2-OD^2}\)

\(\Rightarrow OA=\sqrt{30^2-26,7^2}\approx13,7\left(cm\right)\)

Xét tam giác vuông AOB ta có:

\(AB^2=OA^2+OB^2\)

\(\Rightarrow OB=\sqrt{AB^2-OA^2}\)

\(\Rightarrow OB=\sqrt{17,5^2-13,7^2}\approx10,9\left(cm\right)\)

Độ dài đường chéo BD là:

\(BD=OB+OD=26,7+10,9\approx37,6\left(cm\right)\)

a) \(\left(-12x^{13}y^{15}+6x^{10}y^{14}\right):\left(-3x^{10}y^{14}\right)\)

\(=-12x^{13}y^{15}:-3x^{10}y^{14}+6x^{10}y^{14}:-3x^{10}y^{14}\)

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

b) \(\left(x-y\right)\left(x^2-2x+y\right)-x^3+x^2y\)

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

\(=-2x^2+3xy-y^2\) 

a) \(-12x^{13}\)\(y^{15}\)+\(6x^{10}\)\(y^{14}\):\(-3x^{10}\)\(y^{14}\)

=\(-12x\)\(^{13}\)\(y^{15}\)\(:\)\(-3x^{10}y^{14}\)\(+6x^{10}y^{14}:-3x^{10}y^{14}\)

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

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

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

\(=-2x+y\)

a) \(\left(4x^4-8x^2y^2+12x^5y\right):\left(-4x^2\right)\)

\(=4x^4:-4x^2-8x^2y^2:-4x^2+12x^4y:-4x^2\)

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

b) \(x^2\left(x-y^2\right)-xy\left(1-xy\right)-x^3\)

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

\(=-xy\)

a) (5x³y² - 3x²y + xy) : xy

= 5x³y² : xy + (-3x²y : xy) + xy : xy

= 5x²y - 3x + 1

b) A + 2M = P

A = P - 2M

= 3x³ - 2x²y - xy + 3 - 2.(x³ - x²y + 2xy + 3)

= 3x³ - 2x²y - xy + 3 - 2x³ + 2x²y - 4xy - 6

= (3x³ - 2x³) + (-2x²y + 2x²y) + (-xy - 4xy) + (3 - 6)

= x³ - 5xy - 3

Vậy A = x³ - 5xy - 3

a) \(A:xy\)

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

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

\(=5x^2y-3x+1\)

b) \(A+2M=P\)

\(\Rightarrow A+2\cdot\left(x^3-x^2y+2xy\right)=3x^3-2x^2y-xy+3\)

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

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

\(\Rightarrow A=x^3-4xy+3\)

a) 2(3x - 1) = 10

3x - 1 = 10 : 2

3x - 1 = 5

3x = 5 + 1

3x = 6

x = 6 : 3

x = 2

b) (3x + 4)² - (3x - 1)(3x + 1) = 49

9x² + 24x + 16 - 9x² + 1 = 49

24x + 17 = 49

24x = 49 - 17

24x = 32

x = 32 : 24

x = 4/3

a) \(2\left(3x-1\right)=10\)

\(3x-1=5\)

\(3x=6\)

\(x=2\)

b) \(\left(3x+4\right)^2-\left(3x-1\right)\left(3x+1\right)=49\)

\(9x^2+24x+16-9x^2+1=49\)

\(24x=49-1-16=32\)

\(x=\dfrac{32}{24}=\dfrac{4}{3}\)