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

1 Answer
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 33 and -66. Be careful and always remember to take the negative sign. Multiplying them, we have:
    (3)*(-6)=-18(3)(6)=18

  2. Now, let's take the second pair of like terms: with the variable xx.
    Multiplying xx with x^4x4, we have:
    (x)*(x^4)=x^5(x)(x4)=x5
    Remember, that when the bases are equal, powers can be added up! So, (x)*(x^4)=(x^1)*(x^4)=x^(1+4)=x^5(x)(x4)=(x1)(x4)=x1+4=x5

  3. Now, multiplying the third pair: with the variable yy.
    Multiplying y^5y5 with y^2y2, we have:
    (y^5)*(y^2)=y^(5+2)=y^7(y5)(y2)=y5+2=y7

Thus, by multiplying all three products, we get:
(-18)(x^5)(y^7)=-18x^5y^7(18)(x5)(y7)=18x5y7