# How do you multiply (3xy^5)(-6x^4y^2)?

Oct 26, 2014

Multiplication is fairly simple: all you need to do is multiply the like terms first and multiply your products.

1. First, let's take the constants (the numbers). The two numbers are $3$ and $- 6$. Be careful and always remember to take the negative sign. Multiplying them, we have:
$\left(3\right) \cdot \left(- 6\right) = - 18$

2. Now, let's take the second pair of like terms: with the variable $x$.
Multiplying $x$ with ${x}^{4}$, we have:
$\left(x\right) \cdot \left({x}^{4}\right) = {x}^{5}$
Remember, that when the bases are equal, powers can be added up! So, $\left(x\right) \cdot \left({x}^{4}\right) = \left({x}^{1}\right) \cdot \left({x}^{4}\right) = {x}^{1 + 4} = {x}^{5}$

3. Now, multiplying the third pair: with the variable $y$.
Multiplying ${y}^{5}$ with ${y}^{2}$, we have:
$\left({y}^{5}\right) \cdot \left({y}^{2}\right) = {y}^{5 + 2} = {y}^{7}$

Thus, by multiplying all three products, we get:
$\left(- 18\right) \left({x}^{5}\right) \left({y}^{7}\right) = - 18 {x}^{5} {y}^{7}$