a: \(\left(x+3\right)^3-x\left(3x+1\right)^2+\left(2x+1\right)\left(4x^2-2x+1\right)-3x^2=54\)

\(\Leftrightarrow x^3+9x^2+27x+27-x\left(9x^2+6x+1\right)+8x^3+1-3x^2=54\)

\(\Leftrightarrow9x^3+6x^2+27x+28-9x^3-6x^2-x=54\)

hay x=1

b: Ta có: \(\left(x-3\right)^3-\left(x-3\right)\left(x^2+3x+9\right)+6\left(x+1\right)^2+3x^2=-33\)

\(\Leftrightarrow x^3-9x^2+27x-27-x^3+27+6x^2+12x+6+3x^2=-33\)

hay x=-1

a. (x + 3)³ - x(3x + 1)² + (2x + 1)(4x² - 2x + 1) - 3x² = 54

<=> x³ + 9x² + 27x + 27 - x(9x² + 6x + 1) + 8x³ - 4x² + 2x + 4x² - 2x + 1 - 3x² = 54

<=> x³ + 9x² + 27x + 27 - 9x³ - 6x² - x + 8x³ - 4x² + 2x + 4x² - 2x + 1 - 3x² = 54

<=> x³ - 9x³ + 8x³ + 9x² - 6x² - 4x² + 4x² - 3x² + 27x - x + 2x - 2x = 26

<=> 26x = 26

<=> x = 1

a: Xét ΔHAC vuông tại H và ΔABC vuông tại A có

\(\widehat{C}\) chung

Do đó: ΔHAC~ΔABC

b: ΔABC vuông tại A

=>\(AB^2+AC^2=BC^2\)

=>\(BC^2=15^2+20^2=625\)

=>BC=25

Xét ΔABC vuông tại A có AH là đường cao

nên \(\left\{{}\begin{matrix}BH\cdot BC=BA^2\\AH\cdot BC=AB\cdot AC\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}BH\cdot25=15^2=225\\AH\cdot25=15\cdot20=300\end{matrix}\right.\)

=>BH=9; AH=12

1 being 

2 to do

3 moving

4 to do

5 take/going

6 leaving 

7 repairing

8 playing

9 to use

10 speaking

3 Where was it made?

It was made in England

4 What was it made from?

It was made from wood and stone

6 Does your house have a moat?

Yes, it does

2 True

3 False

4 True

5 False

b

1 It is located on top of a hill

2 They were used to protect people inside the castle

3 They can go upstairs on narrow staircases

4 15000 people visit the castle each day