Factor polynomial completely
8a^2 + 40ab+ 50b^2 =
8a^2 + 40ab+ 50b^2 = 2(4a^2 + 20ab + 25b^2) = 2(2a + 5b)(2a + 5b)
To factor the polynomial 8a^2 + 40ab + 50b^2, we need to find the common factors among the terms.
Step 1: Look for the greatest common factor (GCF) among the coefficients.
In this case, the GCF of 8, 40, and 50 is 2.
Step 2: Look for the GCF among the variables.
We have a^2 and ab, so the GCF would be a.
Step 3: Rewrite the polynomial using the common factors.
Factoring out the GCF from both terms, we get:
2a(4a + 20b + 25b^2)
Step 4: Factor the trinomial (4a + 20b + 25b^2) if possible.
This trinomial can be factored using the grouping method or by recognizing that it is a perfect square trinomial.
Looking at the terms 4a, 20b, and 25b^2, we can see that they have a common factor of 4. Factoring out 4, we get:
2a(4(a + 5b + 6.25b^2))
Now, we have factored the polynomial 8a^2 + 40ab + 50b^2 completely as:
2a(2(a + 5b + 6.25b^2))