Question

8p^2-24; 4c^4-12c^2-3c^3;    x^7y^5-x^5y^7;   14y^3z+35yz^2;  

Answer 1

$1)8p^2-24=8(p^2-3) \\ \\ 2)4c^4-12c^2-3c^3=c^2(4c^2-12-3c) \\\\ 3)x^7y^5-x^5y^7=x^5y^5(x^2-y^2)=x^5y^5(x-y)(x+y)\\\\4)14y^3z+35yz^2=7yz(2y^2+5z)$

Answer 2

Let's simplify each of the given expressions:

1. 8p^2 - 24: This expression can be simplified by factoring out the greatest common factor, which is 8: 8(p^2 - 3)

2. 4c^4 - 12c^2 - 3c^3: There doesn't seem to be a common factor that can be factored out. We can rearrange the terms in descending order of the exponent: 4c^4 - 3c^3 - 12c^2

3. x^7y^5 - x^5y^7: The given expression involves two terms with similar bases but different exponents. We can factor out the common factors, which are x^5 and y^5: x^5y^5(x^2 - y^2) Now, we notice that the expression in parentheses is a difference of squares. We can further factor it: x^5y^5(x - y)(x + y)

4. 14y^3z + 35yz^2: The given expression has a common factor of 7yz. Factoring it out, we get: 7yz(2y^2 + 5z)

I hope this helps! Let me know if you have any further questions.