(3x+1)(3x+8)

2 min read Jun 16, 2024
(3x+1)(3x+8)

Expanding (3x+1)(3x+8)

This article will cover how to expand the expression (3x+1)(3x+8).

Understanding the Problem

The expression (3x+1)(3x+8) represents the product of two binomials. To expand this, we need to multiply each term in the first binomial by each term in the second binomial.

The FOIL Method

A common technique for expanding binomials is the FOIL method. FOIL stands for:

  • First: Multiply the first terms of each binomial.
  • Outer: Multiply the outer terms of the binomials.
  • Inner: Multiply the inner terms of the binomials.
  • Last: Multiply the last terms of each binomial.

Applying FOIL

Let's apply the FOIL method to our expression (3x+1)(3x+8):

  1. First: (3x)(3x) = 9x²
  2. Outer: (3x)(8) = 24x
  3. Inner: (1)(3x) = 3x
  4. Last: (1)(8) = 8

Combining Like Terms

Now we have: 9x² + 24x + 3x + 8

Combining the like terms (24x and 3x): 9x² + 27x + 8

Final Result

Therefore, the expanded form of (3x+1)(3x+8) is 9x² + 27x + 8.

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