(3a-2)^2-(3a+1)(a+5)

2 min read Jun 16, 2024

Simplifying the Expression: (3a - 2)² - (3a + 1)(a + 5)

This article will walk you through the process of simplifying the algebraic expression (3a - 2)² - (3a + 1)(a + 5). We will use the distributive property and the FOIL method to expand and combine terms.

Step 1: Expand the Square

The first term (3a - 2)² represents the square of a binomial. We can expand this using the FOIL method (First, Outer, Inner, Last):

First: (3a)(3a) = 9a²
Outer: (3a)(-2) = -6a
Inner: (-2)(3a) = -6a
Last: (-2)(-2) = 4

Combining these terms, we get: (3a - 2)² = 9a² - 12a + 4

Step 2: Expand the Product

The second term (3a + 1)(a + 5) also represents the product of two binomials. We can expand this using the FOIL method:

First: (3a)(a) = 3a²
Outer: (3a)(5) = 15a
Inner: (1)(a) = a
Last: (1)(5) = 5

Combining these terms, we get: (3a + 1)(a + 5) = 3a² + 16a + 5

Step 3: Combine the Expanded Terms

Now we can substitute the expanded terms back into the original expression:

(3a - 2)² - (3a + 1)(a + 5) = (9a² - 12a + 4) - (3a² + 16a + 5)

Remember to distribute the negative sign to all terms inside the parentheses:

= 9a² - 12a + 4 - 3a² - 16a - 5

Step 4: Simplify by Combining Like Terms

Finally, we combine the terms with the same variable and exponent:

= (9a² - 3a²) + (-12a - 16a) + (4 - 5)

= 6a² - 28a - 1

Therefore, the simplified form of the expression (3a - 2)² - (3a + 1)(a + 5) is 6a² - 28a - 1.