Question

Multiply
- 3r² (r-5r²+2rt)

Answer 1

-3r³ + 15r⁴ - 6r³t

Explanation:

-3r² · r: When you multiply the r into the r², simply add the exponents with eachother. The stand-alone r has an exponent of 1 (any number/letter that doesn't have an exponent, such as 2x has an exponent of 1). Makes -3r³

-3r² · -5r²: First, the numbers. -3 · -5 = 15. Same thing with the exponents from earlier. r² + r² = r⁴ Makes 15r⁴

-3r² · 2rt: First, the numbers. -3 · 2 = -6. Now, the variables. r² · rt = r³t. If it helps, separate the variables stuck together, like this. r² · r · t = r³t. Makes -6r³t

Answer 2

`-3r^(3)+15r^(4)-6r^(3) t`

Explanation:

You can distribute the
`-3r^(2)` to all the terms in the parentheses. This happens by multiplying each term by -3r^{2}

So we get

`-3r^(2)(r)+(-3r^(2) )(-5r^(2) )+(-3r^(2) )(2rt)`

We see that:

`-3r^(2)(r)=-3r^(3) \\(-3r^(2) )(-5r^(2) )=15r^(4) \\(-3r^(2) )(2rt)=-6r^(3) t`

*keep in mind that when multiplying variables or numbers with exponents, we add the exponents together. So
`x^(2) *x^(3) =x^(5)`

If we put all the multiplied terms together, we get:

`-3r^(3) +15r^(4)-6r^(3) t`