Question

How do you simplify `(3x^2y)(10x^5y^3)`?

Answer 1

Multiply each like term in each of the parenthesis. See full explanation below.

Explanation:

We will multiply each common term in parenthesis with the common term in the other parenthesis:

`(color(red)(3)color(blue)(x^2)color(green)(y))(color(red)(10)color(blue)(x^5)color(green)(y^3)) -> (color(red)(3) xx color(red)(10))(color(blue)(x^2) xx color(blue)(x^5))(color(green)(y) xx color(green)(y^3))`

We can multiply the constants and use the rules for exponents to multiply the common terms.

`x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a)+color(blue)(b)`

and

`z = z^(color(red)(1)`

This gives:

`(color(red)(3) xx color(red)(10))(color(blue)(x^2) xx color(blue)(x^5))(color(green)(y) xx color(green)(y^3)) =`

`color(red)(30)color(blue)(x^(2+5))color(green)(y^(1+3)) =`

`color(red)(30)color(blue)(x^7)color(green)(y^4)`