Step By Step Solution:
AIM :
To find factorized form of a² + a + 1/4
TO PROVE
a² + a + 1/4 =
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
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 .
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,
brainly.in/question/8186892
#Hope it helps
# Thanks for asking
- stay blessed-
Answer:
(a 1/2) (a 1/2)
Step-by-step explanation:
Hope it helps!!!!
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Answers & Comments
Factorise
a² + a + 1/4 ?
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} ) ( a + \frac{1}{2} ) + ( a + \frac{1}{2} )](https://tex.z-dn.net/?f=%28%20a%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%29%20%2B%20%28%20a%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%29)
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} ) ( a + \frac{1}{2} ) + ( a + \frac{1}{2} )](https://tex.z-dn.net/?f=%28%20a%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%29%20%2B%20%28%20a%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%29)
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 .
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,
brainly.in/question/8186892
#Hope it helps
# Thanks for asking
- stay blessed-
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!!!!