can someone check these for me please....
problem#4
Directions: Factor each polynomial completely by factoring out any common factors and then factor by grouping. Do not combine like terms.
3a^3+3ab^2+2a^2b+2b^3
My answer:
(a^2+b^2)(3a+2b)
you are correct
To factor the polynomial 3a^3 + 3ab^2 + 2a^2b + 2b^3 completely, we'll follow a two-step process.
Step 1: Factor out any common factors. In this case, the GCF (Greatest Common Factor) is 1, meaning there are no common factors to factor out.
Step 2: Factor by grouping. To do this, we'll group the terms in pairs and look for common factors within each pair.
Group the terms as follows:
(3a^3 + 3ab^2) + (2a^2b + 2b^3)
Now, factor out the common factors in each group:
3a(a^2 + b^2) + 2b(a^2 + b^2)
Notice that (a^2 + b^2) is common to both groups. We can now factor this out:
(a^2 + b^2)(3a + 2b)
So, the completely factored form of the polynomial 3a^3 + 3ab^2 + 2a^2b + 2b^3 is (a^2 + b^2)(3a + 2b).