Answer:
The complete factored form is 4 a^4 b² (7 a² b^4 + 1)
Explanation:
* Lets explain how to solve the problem
- To factorize a binomial ;
# Find the greatest common factors of the coefficient and the variable
# Check the binomial if it is different of two squares or sum of two
cubes or different of two cubes
* Lets solve the problem
∵ 28 a^6 b^6 + 4 a^4 b²
- Lets find the greatest common factors of the coefficients
∵ The greatest factor of 28 and 4 is 4
∴ 28 a^6 b^6 + 4 a^4 b² = 4(7 a^6 b^6 + a^4 b²)
- Lets find the greatest common factors of the variables
∵ The greatest common factors of a^6 and a^4 is a^4
∵ The greatest common factors of b^6 and b² is b²
∴ 4(7 a^6 b^6 + a^4 b²) = 4 a^4 b²(7 a² b^4 + 1)
- Lets check the bracket
∵ There is no common factor in the bracket (7 a² b^4 + 1)
∴ The complete factored form of 28 a^6 b^6 + 4 a^4 b^2 is
4 a^4 b² (7 a² b^4 + 1)