Question

Simplify the given expression. –10xy(4xy3 – 7xy + 9y2)

–40x2y4 – 7x2y2 + 9x2y3

–40x2y4 + 70xy + 90y2

–40x2y4 + 70x2y2 – 90xy3

–40x2y4 – 7xy + 9y2

Answer 1

`\large\boxed{-40x^2y^4+70x^2y^2-90xy^3}`

Explanation:

Use the distributive property a(b + c) = ab + ac:

`-10xy(4xy^3-7xy+9y^2)\\\\=(-10xy)(4xy^3)+(-10xy)(-7xy)+(-10xy)(9y^2)\\\\\text{use}\ a^na^m=a^(n+m)\\\\=-40x^(1+1)y^(1+3)+70x^(1+1)y^(1+1)-90xy^(1+2)\\\\=-40x^2y^4+70x^2y^2-90xy^3`