Question

factorise form of
a²+a+1/4​

Answer 1

a2+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)

Answer 2

The factories form is $a^2+a+\frac{1}{4}=(a+\frac{1}{2})(a+\frac{1}{2})$.

Step-by-step explanation:

Given : Expression $a^2+a+\frac{1}{4}$.

To find : Factories the form of expression ?

Solution :

Expression $a^2+a+\frac{1}{4}$.

To factories add and subtract $(\frac{1}{2})^2$,

$a^2+a+\frac{1}{4}=a^2+a+\frac{1}{4}+(\frac{1}{2})^2-(\frac{1}{2})^2$

Applying identity, $(a+b)^2=a^2+b^2+2ab$

$a^2+a+\frac{1}{4}=(a+\frac{1}{2})^2+\frac{1}{4}-\frac{1}{4}$

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

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

The factories form is $a^2+a+\frac{1}{4}=(a+\frac{1}{2})(a+\frac{1}{2})$.

#Learn more

Exercise 3.5

1. Write 840 in prime factorisation form.

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