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How to Square Brackets in Algebra?

Published in Algebra Expansion 3 mins read

To "square brackets" in algebra means to multiply the expression inside the brackets by itself. This process is often referred to as expanding the square of a binomial or expanding the brackets.

Understanding the Concept

When you see an expression like (a + b)², it doesn't mean a² + b². Instead, it means you have to multiply the entire bracketed expression by itself:

(a + b)² = (a + b) * (a + b)

The video "Expanding Square Brackets | Algebra | Maths | FuseSchool" explains this fundamental principle, stating, "Just like three squared means three times three, the squared here means the bracket times the bracket."

How to Expand Squared Brackets

Here's how to expand squared brackets in algebra, breaking down the process:

  1. Rewrite the Squared Bracket: Change the expression to show the brackets multiplied by themselves. For example, (x + 2)² becomes (x + 2)(x + 2).

  2. Use the FOIL Method (or Distributive Property): Multiply each term in the first bracket by each term in the second bracket.

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

  3. Simplify the Result: Combine any like terms to get the final expanded expression.

Example 1: Expanding (x + 2)²

  • Rewrite: (x + 2)(x + 2)
  • FOIL:
    • First: x * x = x²
    • Outer: x * 2 = 2x
    • Inner: 2 * x = 2x
    • Last: 2 * 2 = 4
  • Combine: x² + 2x + 2x + 4
  • Simplify: x² + 4x + 4

Example 2: Expanding (3x - 1)²

  • Rewrite: (3x - 1)(3x - 1)
  • FOIL:
    • First: 3x * 3x = 9x²
    • Outer: 3x * -1 = -3x
    • Inner: -1 * 3x = -3x
    • Last: -1 * -1 = 1
  • Combine: 9x² - 3x - 3x + 1
  • Simplify: 9x² - 6x + 1

Key Takeaways

  • Squaring a bracket involves multiplying the expression within the brackets by itself.
  • The FOIL method (or distributive property) helps ensure all terms are properly multiplied.
  • Always simplify the final expression by combining like terms.
Step Description Example
Rewrite Write the squared bracket as two separate brackets multiplied. (a-3)² → (a-3)(a-3)
Multiply Multiply using FOIL or the distributive property. (aa) + (a-3) + (-3a) + (-3-3)
Simplify Combine like terms. a² -3a -3a + 9 = a² - 6a + 9

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