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

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Answer 1 · 2014-10-26T20:43:19

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

First, let's take the constants (the numbers). The two numbers are $3$ $3$ and $- 6$ $-6$ . Be careful and always remember to take the negative sign. Multiplying them, we have:
$(3) \cdot (- 6) = - 18$ $(3)*(-6)=-18$
Now, let's take the second pair of like terms: with the variable $x$ $x$ .
Multiplying $x$ $x$ with $x^{4}$ $x^4$ , we have:
$(x) \cdot (x^{4}) = x^{5}$ $(x)*(x^4)=x^5$
Remember, that when the bases are equal, powers can be added up! So, $(x) \cdot (x^{4}) = (x^{1}) \cdot (x^{4}) = x^{1 + 4} = x^{5}$ $(x)*(x^4)=(x^1)*(x^4)=x^(1+4)=x^5$
Now, multiplying the third pair: with the variable $y$ $y$ .
Multiplying $y^{5}$ $y^5$ with $y^{2}$ $y^2$ , we have:
$(y^{5}) \cdot (y^{2}) = y^{5 + 2} = y^{7}$ $(y^5)*(y^2)=y^(5+2)=y^7$

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

How do you multiply (3xy5)(−6x4y2)(3xy^5)(-6x^4y^2)?