Multiply. (x+2)(x-2)
my answer is: x^2-4
Factor completely. 3(x-2)^2-3(x-2)-6
MY answer: 3(x-4)(x-1)
Factor 9x(x-7y)-6(x-7y)
My answer is: (9x-6)(x-7y)
Divide: (x^3+2x^2+x+12)/(x+3)
My anwer is: x^2-x+4
Looks OK!
Let's check your answers one by one:
1. To multiply (x+2)(x-2), you can use the FOIL method, which stands for First, Outer, Inner, Last. Multiply the terms in the first parentheses with the terms in the second parentheses:
First: x * x = x^2
Outer: x * -2 = -2x
Inner: 2 * x = 2x
Last: 2 * -2 = -4
Now, combine the like terms -2x and 2x to simplify the expression:
x^2 - 2x + 2x - 4
The terms -2x and 2x cancel each other out, leaving us with:
x^2 - 4
So, your answer of x^2 - 4 is correct.
2. To factor 3(x-2)^2-3(x-2)-6, we can notice that there is a common factor of (x-2) in all three terms. By factoring that out, we get:
3(x-2)((x-2) - 1) - 6
Simplifying further:
3(x-2)(x-2 - 1) - 6
3(x-2)(x-3) - 6
So, your answer of 3(x-4)(x-1) is incorrect. The correct factored form is 3(x-2)(x-3) - 6.
3. To factor 9x(x-7y)-6(x-7y), we can notice that there is a common factor of (x-7y) in both terms. By factoring that out, we get:
(x-7y)(9x - 6)
So, your answer of (9x-6)(x-7y) is correct.
4. To divide (x^3+2x^2+x+12) by (x+3), you can use long division or synthetic division. Let's use long division:
x+3 │ x^3 + 2x^2 + x + 12
By dividing x^3 by x, we get x^2. Then, we multiply x+3 by x^2 to get x^3 + 3x^2. Subtracting that from the original equation:
x^2 + x + 12
______________________
x+3 │ x^3 + 2x^2 + x + 12
- (x^3 + 3x^2)
_______________
- x^2 + x
By dividing -x^2 by x, we get -x. Then, we multiply x+3 by -x to get -x^2 - 3x. Subtracting that from the previous step:
- x + 12
______________________
x+3 │ x^3 + 2x^2 + x + 12
- (x^3 + 3x^2)
_______________
- x^2 + x
- (-x^2 - 3x)
______________
4x + 12
By dividing 4x by x, we get 4. Then, we multiply x+3 by 4 to get 4x + 12. Subtracting that from the previous step:
0
______________________
x+3 │ x^3 + 2x^2 + x + 12
- (x^3 + 3x^2)
_______________
- x^2 + x
- (-x^2 - 3x)
______________
4x + 12
- (4x + 12)
______________
0
Since the remainder is zero, we have successfully divided the expression. The quotient is x^2 - x + 4.
So, your answer of x^2 - x + 4 is correct.
Great job on most of your answers! If you have any more questions or need further explanations, feel free to ask!