What did you buy?

What did you buy? 

a) \(=x^3-8\)

b) \(=\left(2x\right)^3+1=8x^3+1\)

c) \(=1-\left(\dfrac{x}{2}\right)^3=1-\dfrac{x^3}{8}\)

d) \(=y^3-\left(\dfrac{x}{y}\right)^3\)

a) \(M=x^3+27\)

b) \(N=1-\left(3x\right)^3=1-27x^3\)

c) \(P=x^3-\left(\dfrac{1}{2}\right)^3=x^3-\dfrac{1}{8}\)

d) \(Q=\left(2x\right)^3+\left(3y\right)^3=8x^3+27y^3\)

a: (x-2)(x^2+2x+4)=x^3-2^3=x^3-8

b; (2x+1)(4x^2-2x+1)

=(2x)^3+1^3

=8x^3+1

c: (1-x/2)(1+x/2+x^2/4)

=1-(x/2)^3

=1-1/8x^3

d: (y-x/y)(y^2+x+x^2/y^2)

=y^3-(x/y)^3

=y^3-x^3/y^3

a: (x+3)(x^2-3x+9)

=x^3+3^3

=x^3+27

b: (1-3x)(1+3x+9x^2)

=1^3-(3x)^3

=1-27x^3

c: (x-1/2)(x^2+1/2x+1/4)

=x^3-(1/2)^3

=x^3-1/8

d: (2x+3y)(4x^2-6xy+9y^2)

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

=8x^3+27y^3

độ dài của bán kính là

`15,7:3,14:2=2,5(cm)`

2.5

\(x^4-9x^3+x^2-9x\\ =x^3\left(x-9\right)+x\left(x-9\right)\\ =\left(x^3+x\right)\left(x-9\right)=x\left(x^2+1\right)\left(x-9\right)\\ ---\\ x^2-9-x^2\left(x^2-9\right)\\ =\left(x^2-9\right)-x^2\left(x^2-9\right)\\ =\left(x^2-9\right)\left(1-x^2\right)=\left(1-x\right)\left(1+x\right)\left(x-3\right)\left(x+3\right)\\ ---\\ xz+yz-5x-5y=z\left(x+y\right)-5\left(x+y\right)\\ =\left(z-5\right)\left(x+y\right)\\ ---\\ x^3-2x+y^3-2y\\ =\left(x^3+y^3\right)-2\left(x+y\right)=\left(x+y\right)\left(x^2-xy+y^2\right)-2\left(x+y\right)\\ =\left(x+y\right)\left(x^2-xy+y^2-2\right)\)

\(45+x^3-5x^2-9x\\ =x^2\left(x-5\right)-9\left(x-5\right)\\ =\left(x^2-9\right)\left(x-5\right)=\left(x-3\right)\left(x+3\right)\left(x-5\right)\\ ---\\ x^2-y^2-2x-2y\\ =\left(x^2-y^2\right)-\left(2x+2y\right)\\ =\left(x-y\right)\left(x+y\right)-2\left(x+y\right)\\ =\left(x+y\right)\left(x-y-2\right)\\ ---\\ x^3+7x^2-4x-28\\ =x^2\left(x+7\right)-4\left(x+7\right)\\ =\left(x+7\right)\left(x^2-4\right)=\left(x+7\right)\left(x-2\right)\left(x+2\right)\\ ---\\ 8x^3-y^3-4x+2y=\left(8x^3-y^3\right)-2\left(2x-y\right)\\ =\left(2x-y\right)\left(4x^2+2xy+y^2\right)-2\left(2x-y\right)\\ =\left(2x-y\right)\left(4x^2+2xy+y^2-2\right)\)

1. If we are able to collect solar energy, we will be sure to have enough power.

2. Energy from the wind has been used for centuries to move ships and pump water.

3. Recently, wind has been used to generate electricity.

4. For a long time, people have used water to power machines.

5. Today, water power is mostly used to generate electricity.

tích bán kính hình tròn là

`153,86:3,14=49(cm)`

vì `49=7xx7` nên độ dài của bán kính là `7(cm)`

độ dài của đường kính là

`7xx2=14(cm)`

Ta có  \(153,86:3,14=49\)

mà \(49=7.7\)

\(\Rightarrow\) Bán kính \(=7\left(cm\right)\)

Đường Kính \(=2.7=14\left(cm\right)\)

Đường kính là 49cm