factor completely
1. x^3-9x^2
2. 36x^6-49x^4
1) x^2(x-9) I suspect you copied this wrong.
2) The second is a difference of squares, which when you factor, you will see a second set of difference of squares.
To factor the given expressions completely, we can use the factoring techniques.
1. Let's factor the expression x^3 - 9x^2.
Notice that both terms have a common factor of x^2. We can factor out x^2 from both terms:
x^3 - 9x^2 = x^2(x - 9)
So the factored form of the expression x^3 - 9x^2 is x^2(x - 9).
2. Now let's factor the expression 36x^6 - 49x^4.
This expression consists of two terms. Notice that both terms have a common factor of x^4. We can factor out x^4 from both terms:
36x^6 - 49x^4 = x^4(36x^2 - 49)
The expression 36x^2 - 49 is a difference of squares. It can be factored by using the formula a^2 - b^2 = (a + b)(a - b), where a = 6x and b = 7:
36x^2 - 49 = (6x)^2 - 7^2 = (6x + 7)(6x - 7)
Putting it all together, the factored form of the expression 36x^6 - 49x^4 is x^4(6x + 7)(6x - 7).
So, the factored forms are:
1. x^3 - 9x^2 = x^2(x - 9)
2. 36x^6 - 49x^4 = x^4(6x + 7)(6x - 7)