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

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

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

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

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