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(a+b)^2-a^2+b^2 Factorise

2 min read Jun 16, 2024
(a+b)^2-a^2+b^2 Factorise

Factoring (a + b)^2 - a^2 + b^2

This article will guide you through the process of factoring the expression (a + b)^2 - a^2 + b^2.

Understanding the Expression

The expression involves squaring a binomial, subtracting a squared term, and adding another squared term. Let's break it down:

  • (a + b)^2: This is a binomial squared, which expands to a^2 + 2ab + b^2 using the formula (x + y)^2 = x^2 + 2xy + y^2.
  • - a^2: This is a simple squared term.
  • + b^2: This is another simple squared term.

The Factorization Process

  1. Expand the binomial: Begin by expanding the squared term:

    (a + b)^2 - a^2 + b^2 = (a^2 + 2ab + b^2) - a^2 + b^2

  2. Simplify by combining like terms:

    (a^2 + 2ab + b^2) - a^2 + b^2 = 2ab + 2b^2

  3. Factor out the common factor: Notice that both terms in the expression have 2b in common. Factor it out:

    2ab + 2b^2 = 2b(a + b)

Final Result

Therefore, the factored form of the expression (a + b)^2 - a^2 + b^2 is 2b(a + b).

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