Question

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Factorise the equation...

4x² + 4bx - (a² - b²) = 0​

Answer 1

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Answer 2

Answer :-

★ x = ½(a - b)

★ Concept :-

• The concept used here is of splitting the middle term. According to this, when we find some terms in a equation nearly similar to others, we take those terms in common to determine the whole term into a factorised form.

★ Solution :-

Given,

✏ 4x² + 4bx - (a² - b²) = 0

On opening the bracket, we get,

✏ 4x² + 4bx - a² + b² = 0

Now taking the common terms together, we get,

✏ (4x² + 4bx + b²) - a² = 0

• Using the identity of,

(x + y) ² = x² + y² + 2xy

We get,

✏ (2x + b)² - a² = 0

(Since, (2x + b)² = 4x² + 4bx + b² )

Now, let us transpose a² to RHS,

✏ (2x + b)² = a²

✏ (2x + b) = √a²

✏ 2x + b = a

✏ 2x = a - b

✏ $x \: \: = \: \: \dfrac{a \: - \: b}{2}$

Hence we get, that value of,

x = ½ (a - b)

★ More to Know :-

• Factorisation - It is the method of reducing complex equations into smaller and simpler equations by simple algebraic methods.

• Polynomial - It is a equation made by the use of variables and consonants to determine a value. Variables are usually derived from consonants.

• Linear Equations - These are equations made by the use of variable, where the output or value of of variable is given and we have to find either of them.