factor:
1. 6x^2y+4xy^3+10x^4y^4
2. 27m^3-8
3. 6n^8-11n^4-10
4. nx^2+x^2-9n-9
1. take out the common factor 2xy
2. difference of two cubes.
3. let n^4=u^2
6u^2-11u -10
then factor.
4. two common factors
x^2(n+1) -9(n+1)
(n+1)(x^2-9) then the last term can be factored as a difference of two squares.
thankyou
To factor the given expressions, we need to find the common factors and then apply appropriate factoring methods. Let's solve each expression step by step:
1. 6x^2y + 4xy^3 + 10x^4y^4:
- We need to look for common factors in each term. Here, the common factor is 2xy.
- Factoring out the common factor:
2xy(3x + 2y^2 + 5x^3y^3)
2. 27m^3 - 8:
- This is a difference of cubes, which can be factored using the formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2)
- Factoring:
(3m - 2)(9m^2 + 6m + 4)
3. 6n^8 - 11n^4 - 10:
- This expression does not have any common factors.
- It cannot be factored any further using simple methods. So, it remains as it is.
4. nx^2 + x^2 - 9n - 9:
- We group the terms with similar factors.
- Factoring:
(n + 1)(x^2 - 9) = (n + 1)(x + 3)(x - 3)
Remember, factoring requires practice and identifying common factors or applying specific formulas.