MATH SOLVE

3 months ago

Q:
# find the complete factored form of the polynomial 28 a^6 b^6 + 4 a^4 b^2

Accepted Solution

A:

Answer:The complete factored form is 4 a^4 b² (7 a² b^4 + 1)Step-by-step 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)