Question

Tính: a+b=10 và a.b=-36
a) a.(2+b)+b(a+2)
b)a²+b²
c)a³+b³

Answer 1

`a)a(2+b)+b(a+2)`

`=2a+ab+ab+2b`

`=2(a+b)+2ab`

`=2.10+2.(-36)`

`=20-72=-52`

`b)a^2+b^2`

`=(a+b)^2-2ab`

`=10^2-2.(-36)`

`=100+72=172`

`c)a^3+b^3`

`=(a+b)(a^2-ab+b^2)`

`=10[(a+b)^2-3ab]`

`=10[10^2-3.(-36)]`

`=10(100+108)`

`=10.208=2080`

Answer 2

a, \(=>2a+ab+ab+2b=2\left(a+b+ab\right)=2\left(10-36\right)=-52\)

b, \(a^2+b^2=a^2+2ab+b^2-2ab=\left(a+b\right)^2-2ab=\left(10\right)^2-2\left(-36\right)=172\)

c, \(a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)=10\left[\left(a+b\right)^2-3ab\right]\)

\(=10\left[10^2-3\left(-36\right)\right]=2080\)

Answer 3

\(a\left(2+b\right)+b\left(a+2\right)=2ab+2\left(a+b\right)=2.\left(-36\right)+2.10=-52\)

\(a^2+b^2=\left(a+b\right)^2-2ab=172\)

\(a^3+b^3=\left(a+b\right)^3-3ab\left(a+b\right)=2080\)

Answer 4

c) \(a^3+b^3=\left(a+b\right)^3-3ab\left(a+b\right)=10^3-3\cdot\left(-36\right)\cdot10=1000+1080=2080\)