how do you solve the problem (x^2-y)^3
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That depends on what the question is.  You need to say what you want done with it.  If you want it expanded then:

You can multiply this out and you should get the right answer, but there's an easier way.

.

Pascal's Triangle:

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1

When you have something like (a+b)^n it works like this:

(a+b)^0 = 1

(a+b)^1 = a + b

(a+b)^2 = a^2 + 2ab + b^2

Look at the numbers in front of each set of letters:

1
1 1
1 2 1

That's Pascal's Triangle.

See how (a+b)^2 made the row in the triangle 1 2 1?

Whatever row in the triangle has your exponent, that's the row to use.  If you had (a+b)^4 it would be 1 4 6 4 1 or:

a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4.

.

In this problem (x^2 - y)^3 it's like (a+b)^3, so we would use the row in the triangle with 1 3 3 1.  (a+b)^3 would make this:

a^3 + 3a^2b + 3ab^2 + b^3

In this problem we have x^2 instead of a, and -y instead of b, so we replace the a and b stuff with x and y stuff like this:

(x^2)^3 + 3(x^2)^2(-y) + 3(x^2)(-y)^2 + (-y)^3

x^6 - 3x^4y + 3x^2y^2 - y^3
by Level 13 User (103k points)

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