Answer:
2 (2 x + 5)^2
Step-by-step explanation:
Factor the following:
8 x^2 + 40 x + 50
Hint: | Factor out the greatest common divisor of the coefficients of 8 x^2 + 40 x + 50.
Factor 2 out of 8 x^2 + 40 x + 50:
2 (4 x^2 + 20 x + 25)
Hint: | Factor 4 x^2 + 20 x + 25 by finding factors of 4×25 whose sum is 20.
Factor the quadratic 4 x^2 + 20 x + 25. The coefficient of x^2 is 4 and the constant term is 25. The product of 4 and 25 is 100. The factors of 100 which sum to 20 are 10 and 10. So 4 x^2 + 20 x + 25 = 4 x^2 + 10 x + 10 x + 25 = 5 (2 x + 5) + 2 x (2 x + 5):
2 5 (2 x + 5) + 2 x (2 x + 5)
Hint: | Factor common terms from 5 (2 x + 5) + 2 x (2 x + 5).
Factor 2 x + 5 from 5 (2 x + 5) + 2 x (2 x + 5):
2 (2 x + 5) (2 x + 5)
Hint: | Combine products of like terms.
(2 x + 5) (2 x + 5) = (2 x + 5)^2:
Answer: 2 (2 x + 5)^2
