(6a+5)(5a+3) In Standard Form

2 min read Jun 16, 2024

Expanding and Simplifying (6a+5)(5a+3)

This article will guide you through the process of expanding and simplifying the expression (6a+5)(5a+3), ultimately presenting it in standard form.

Understanding the Problem

We are given a product of two binomials: (6a+5) and (5a+3). Our goal is to rewrite this product as a polynomial in standard form.

Expanding the Product

To expand the product, we can use the distributive property (also known as FOIL - First, Outer, Inner, Last).

First: Multiply the first terms of each binomial: (6a)(5a) = 30a²
Outer: Multiply the outer terms of the binomials: (6a)(3) = 18a
Inner: Multiply the inner terms of the binomials: (5)(5a) = 25a
Last: Multiply the last terms of each binomial: (5)(3) = 15

This gives us: 30a² + 18a + 25a + 15

Simplifying to Standard Form

Now we combine like terms:

30a² + (18a + 25a) + 15 30a² + 43a + 15

The Final Result

Therefore, the expression (6a+5)(5a+3) in standard form is 30a² + 43a + 15.