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(3x-4)^2 Expand And Simplify

2 min read Jun 16, 2024
(3x-4)^2 Expand And Simplify

Expanding and Simplifying (3x-4)^2

This article will guide you through the process of expanding and simplifying the expression (3x - 4)^2.

Understanding the Concept

The expression (3x - 4)^2 represents squaring the entire binomial (3x - 4). This means multiplying the binomial by itself:

(3x - 4)^2 = (3x - 4) * (3x - 4)

Expanding the Expression

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

FOIL Method:

  1. First: Multiply the first terms of each binomial: (3x) * (3x) = 9x^2
  2. Outer: Multiply the outer terms: (3x) * (-4) = -12x
  3. Inner: Multiply the inner terms: (-4) * (3x) = -12x
  4. Last: Multiply the last terms: (-4) * (-4) = 16

This gives us: 9x^2 - 12x - 12x + 16

Simplifying the Expression

Combine the like terms: 9x^2 - 24x + 16

Final Result

Therefore, the expanded and simplified form of (3x - 4)^2 is 9x^2 - 24x + 16.

Key Points

  • Remember that squaring a binomial means multiplying it by itself.
  • The FOIL method helps to ensure that all terms are multiplied correctly.
  • Always simplify the expression by combining like terms.

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