a) \(x y + y^{2} - x - y\)

\(= \left(\right. x y + y^{2} \left.\right) - \left(\right. x + y \left.\right)\)

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

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

b) \(\left(\left(\right. x^{2} y^{2} - 8 \left.\right)\right)^{2} - 1\)

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

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

\(= \left(\right. x y - 3 \left.\right) \left(\right. x y + 3 \left.\right) \left(\right. x^{2} y^{2} - 7 \left.\right) .\)

\(= \left(\right. x - 1 \left.\right) \left(\right. x + 8 \left.\right) .\)

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)

a) Xét tứ giác ABCD ta có:

\(\hat{A} + \hat{B} + \hat{C} + \hat{D} = 36 0^{o}\)

\(\Rightarrow \hat{D} = 36 0^{o} - 10 2^{o} - 10 2^{o} - 10 2^{o}\)

\(\Rightarrow \hat{D} = 5 4^{o}\) 

b) Xét tam giác vuông AOD ta có:

\(A D^{2} = O D^{2} + O A^{2}\)

\(\Rightarrow O A = \sqrt{A D^{2} - O D^{2}}\)

\(\Rightarrow O A = \sqrt{3 0^{2} - 26 , 7^{2}} \approx 13 , 7 \left(\right. c m \left.\right)\)

Xét tam giác vuông AOB ta có:

\(A B^{2} = O A^{2} + O B^{2}\)

\(\Rightarrow O B = \sqrt{A B^{2} - O A^{2}}\)

\(\Rightarrow O B = \sqrt{17 , 5^{2} - 13 , 7^{2}} \approx 10 , 9 \left(\right. c m \left.\right)\)

Độ dài đường chéo BD là:

\(B D = O B + O D = 26 , 7 + 10 , 9 \approx 37 , 6 \left(\right. c m \left.\right)\)

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

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

\(= 4 x^{3} y - 2.\)

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

\(= x \left(\right. x^{2} - 2 x + y \left.\right) - y \left(\right. x^{2} - 2 x + y \left.\right) - x^{3} + x^{2} y\)

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

\(= - 2 x^{2} + 3 x y - y^{2} .\)