Final answer:
To find the complete factored form of the polynomial 40a^3b^2 + 45a^2b^6, we can find the greatest common factor (GCF) of the terms and factor it out. The factored form is 5a^2b^2(8a + 9b^4).
Step-by-step explanation:
The given expression, 40a3b2 + 45a2b6, is a polynomial in two variables a and b. To find the complete factored form, we can look for the greatest common factor (GCF) of the terms. The GCF of 40a3b2 and 45a2b6 is 5a2b2. Factoring out the GCF, we get:
40a3b2 + 45a2b6 = 5a2b2(8a + 9b4)