Question

Factorise a2 + a + 1/4​

Answer 1

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Factorise

a² + a + 1/4​ ?

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Step By Step Solution:

METHOD 1 { Formula Method }

AIM :

To find factorized form of a² + a + 1/4

TO PROVE

a² + a + 1/4  = $( a + \frac{1}{2} ) + ( a + \frac{1}{2} )$

Let us prove it,

Given Expression = a² + a + 1/4

To Factorize this let us add and subtract (1/2) on the given expression

a² + a + 1/4

= a² + a + 1/4 +(1/2) - (1/2)

Let us apply some identity of find the correct answer

The identity is,

(a + b)² = a²+b²+2 ab

Let us compare this values according to the derived equation

a = a

b = 1/2

Then let us apply

a² + a + 1/4 = (a + 1/2 )² + 1/4 - 1/4

Then,

1/4 gets cancelled

a² + a + 1/4 = (a + 1/2 )²

a² + a + 1/4 = $( a + \frac{1}{2} ) + ( a + \frac{1}{2} )$

METHOD 2: { By taking Common}

AIM :

To find factorized form of a² + a + 1/4

Let us take common from given equation

From the given question a can be written as,

a = 1/2 a + 1/2 a

Let us apply in equation

a² + a + 1/4  = a² + 1/2 a + 1/2 a + 1/4

                    = (a² + 1/2 a) + (1/2 a + 1/4)

                    = a ( a + 1/2 ) + 1/2 ( a+ 1/2 )

                    = (a +1/2) (a+ 1/2 )

Hence proved .

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Factorization can be easily done through these formulas

These fomulas play great role in factorization

Let us see some of those formulas

✧ (a + b)² = a² + 2ab + b²

✧ (a – b)² = a² – 2ab + b²

✧ (a + b) (a – b) = a² -b²

✧  (x + a) (x + b) = x² + (a + b) x + ab.

✧ (x + a) (x – b) = x² + (a – b) x – ab.

✧ (x – a) (x + b) = x² + (b – a) x – ab.

For more explanation refer,

https://brainly.in/question/8186892

#Hope it helps

# Thanks for asking

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Answer 2

Answer:

(a 1/2) (a 1/2)

Step-by-step explanation:

a² + a + 1/4  = a² + 1/2 a + 1/2 a + 1/4

                    = (a² + 1/2 a) + (1/2 a + 1/4)

                    = a ( a + 1/2 ) + 1/2 ( a+ 1/2 )

                    = (a +1/2) (a+ 1/2 )

Hope it helps!!!!