Question

1.(a-b)(a²+an+b²)
2.(x²-y²)(5x+ 0,5y)
3.(x²+2xy+y²)(x-y)

Answer 1

a) (a−b)(a²+an+b²)=(a+−b)(a²+an+b²)=(a)(a²)+(a)(an)+(a)(b²)+(−b)(a²)+(−b)(an)+(−b)(b²)=a³+a²n+ab²−a²b−abn−b³=a³−a²b+a²n+ab²−abn−b³

b) (x²−y²)(5x+0.5y)=(x²+−y²)(5x+0.5y)=(x²)(5x)+(x²)(0.5y)+(−y²)(5x)+(−y²)(0.5y)=5x³+0.5x²y−5xy²−0.5y³

c) (x²+2xy+y²)(x−y)=(x²+2xy+y²)(x+−y)=(x²)(x)+(x²)(−y)+(2xy)(x)+(2xy)(−y)+(y²)(x)+(y²)(−y)=x³−x²y+2x²y−2xy²+xy²−y³=x³+x²y−xy²−y³