a^2+a+1/4 factories
Answers
The factories form is a^2+a+\frac{1}{4}=(a+\frac{1}{2})(a+\frac{1}{2})a
2
+a+
4
1
=(a+
2
1
)(a+
2
1
) .
Step-by-step explanation:
Given : Expression a^2+a+\frac{1}{4}a
2
+a+
4
1
.
To find : Factories the form of expression ?
Solution :
Expression a^2+a+\frac{1}{4}a
2
+a+
4
1
.
To factories add and subtract (\frac{1}{2})^2(
2
1
)
2
,
a^2+a+\frac{1}{4}=a^2+a+\frac{1}{4}+(\frac{1}{2})^2-(\frac{1}{2})^2a
2
+a+
4
1
=a
2
+a+
4
1
+(
2
1
)
2
−(
2
1
)
2
Applying identity, (a+b)^2=a^2+b^2+2ab(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+
4
1
=(a+
2
1
)
2
+
4
1
−
4
1
a^2+a+\frac{1}{4}=(a+\frac{1}{2})^2a
2
+a+
4
1
=(a+
2
1
)
2
a^2+a+\frac{1}{4}=(a+\frac{1}{2})(a+\frac{1}{2})a
2
+a+
4
1
=(a+
2
1
)(a+
2
1
)
The factories form is a^2+a+\frac{1}{4}=(a+\frac{1}{2})(a+\frac{1}{2})a
2
+a+
4
1
=(a+
2
1
)(a+
2
1
) .
Answer:
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