Final answer:
By using the distributive property, the multiplication of binomials (5x + 3)(2x + 5) results in 10x^2 + 31x + 15, which correlates with option b.
Step-by-step explanation:
To multiply the binomials (5x + 3)(2x + 5), we apply the distributive property, also known as the FOIL method (First, Outer, Inner, Last) to expand the product:
First: Multiply the first terms in each binomial: 5x * 2x = 10x^2.Outer: Multiply the outer terms in the binomials: 5x * 5 = 25x.Inner: Multiply the inner terms in the binomials: 3 * 2x = 6x.Last: Multiply the last terms in each binomial: 3 * 5 = 15.
Now, combine like terms (25x and 6x):
10x^2 + 25x + 6x + 15 = 10x^2 + (25x + 6x) + 15 = 10x^2 + 31x + 15.
Therefore, the product of the binomials (5x + 3)(2x + 5) is 10x^2 + 31x + 15, which corresponds to option b.