How do I simplify these?

Question

1. (xy^2)^3 (x^2y)^2 + (x^3y^4)(x^2y^2)^2
2. (3x^2)(3y^2)+ 3x^2y - (3xy)^2 - 3xy^2

Answer 1

1. (xy^2)^3 (x^2y)^2 + (x^3y^4)(x^2y^2)^2
(x^3y^6)(x^4y^2) + (x^3y^4)(x^4y^4)
x^7y^8 + x^7y^8
2x^7y^8

2. (3x^2)(3y^2)+ 3x^2y - (3xy)^2 - 3xy^2
9x^2y^2 + 3x^2y - 9x^2y^2 - 3xy^2
9x^2y^2 - 9x^2y^2 + 3x^2y - 3xy^2
3x^2y - 3xy^2

Simplifying is fun.

Barjesse37

Answer 2

As in the order of operations, start with the exponents.
(x(y^2))^3 = [(x^3)(y^6)], for example. Multiply the outside exponent by each individual variable exponent.

Is that (x^2y)^2 a typo? Separating each variable with its exponent in parenthesis would help. The way you've typed it, I'm not sure how to read it.

Just remember, distribute exponents first, then multiply, then add or subtract. Good luck!

Answer 3

You need to apply the rule: (xy)^n = x^ny^n throughout this question.

I will do the first one only. Try to follow my steps.

1. (xy^2)^3 (x^2y)^2 + (x^3y^4)(x^2y^2)^2

(xy^2)^3 becomes x^3y^6

(x^2y)^2 becomes x^4y^2

We now multiply (x^3y^6) times (x^4y^2).

So, (x^3y^6) times (x^4y^2) = x^7y^8.

Do you see what I am doing?

Next:

(x^3y^4) times (x^2y^2)^2

I will simplify (x^2y^2)^2 first and then multiply the result by (x^3y^4).

So, (x^2y^2)^2 becomes x^4y^4.

Next:

(x^3y^4) times (x^4y^4) = x^7y^8.

Now we put everything together to complete our simplification.

x^7y^8 + x^7y^8 = 2(x^7)(y^8).

Got it?

Guido

Answer 4

1. 2(x^7y^8)

2. 3x^2y-3xy^2

Answer 5

multiply them.