Introduction to the perfect square formula :
In the mathematics, the perfect square is sometimes known as a square number. The perfect square is the integer square or also represented as the perfect square is the product of some of the integer with itself. The perfect square numbers are only the positive numbers not having the negative numbers. The positive values are not having perfect square divisors except only one is known as square free.
Formula for perfect square formula :
The regular notation for the perfect square formula is the perfect square of the number n not the n x n that is not the product of the number n.The model of square can be used to number systems.
Explanation of the perfect square formula:
In the arithmetic we have the following perfect squares like,`1^2=1,2^2=4,3^2=9,..`
In this way we can able to make the perfect square in the algebra. It is explained in the following ways, take the expansion of `(a+b)^2`
`(a+b)^2=(a+b)(a+b)=a(a+b)+b(a+b)=a^2 +ab+ba+b^2=a^2+b^2+2ab`
`a^2+b^2+2ab` it is the perfect square formula of the (a+b).
the expansion of `(a-b)^2`
`(a-b)^2=(a-b)(a-b)=a(a-b)-b(a-b)=a^2-ab-ba+b^2=a^2+b^2-2ab`
`a^2+b^2-2ab` it is the perfect square formula of the ( a-b).
Geometrical representation:
Consider the square of a side (a + b) units .
Area of the square `=(side)^2=(a+b)^2`
Area of the square is same as the areas of the four rectangles.so it can be written as,
Area of the square `= a^2+ab+ab+b^2=a^2+2ab+b^2.`
Understanding Area of Square Formula is always challenging for me but thanks to all math help websites to help me out.
Example 1 for the perfect square formula:
To solve the following `(x+5)^2`
Solution:
Given,
`(x+5)^2 =(x+5)(x+5)=x(x+5)+5(x+5)=x^2+5x+5x+25=x^2+10x+25.`
The result of the equation is `x^2+10x+25.`
Example 2 for the perfect square formula:
To solve the following `(a+2)^2`
Solution:
Given,
`(a+2)^2 =(a+2)(a+2)=a(a+2)+2(a+2)=a^2+2a+2a+4=a^2+4a+4.`
The result of the equation is` a^2+4a+4.`
Example 3 for the perfect square formula:
To solve the following `(a-2)^2`
Solution:
Given,
`(a-2)^2 =(a-2)(a-2)=a(a-2)-2(a-2)=a^2-2a-2a+4=a^2-4a+4.`
The result of the equation is` a^2-4a+4.`
In the mathematics, the perfect square is sometimes known as a square number. The perfect square is the integer square or also represented as the perfect square is the product of some of the integer with itself. The perfect square numbers are only the positive numbers not having the negative numbers. The positive values are not having perfect square divisors except only one is known as square free.
Formula for perfect square formula :
The regular notation for the perfect square formula is the perfect square of the number n not the n x n that is not the product of the number n.The model of square can be used to number systems.
Explanation of the perfect square formula:
In the arithmetic we have the following perfect squares like,`1^2=1,2^2=4,3^2=9,..`
In this way we can able to make the perfect square in the algebra. It is explained in the following ways, take the expansion of `(a+b)^2`
`(a+b)^2=(a+b)(a+b)=a(a+b)+b(a+b)=a^2 +ab+ba+b^2=a^2+b^2+2ab`
`a^2+b^2+2ab` it is the perfect square formula of the (a+b).
the expansion of `(a-b)^2`
`(a-b)^2=(a-b)(a-b)=a(a-b)-b(a-b)=a^2-ab-ba+b^2=a^2+b^2-2ab`
`a^2+b^2-2ab` it is the perfect square formula of the ( a-b).
Geometrical representation:
Consider the square of a side (a + b) units .
Area of the square `=(side)^2=(a+b)^2`
Area of the square is same as the areas of the four rectangles.so it can be written as,
Area of the square `= a^2+ab+ab+b^2=a^2+2ab+b^2.`
Understanding Area of Square Formula is always challenging for me but thanks to all math help websites to help me out.
Example 1 for the perfect square formula:
To solve the following `(x+5)^2`
Solution:
Given,
`(x+5)^2 =(x+5)(x+5)=x(x+5)+5(x+5)=x^2+5x+5x+25=x^2+10x+25.`
The result of the equation is `x^2+10x+25.`
Example 2 for the perfect square formula:
To solve the following `(a+2)^2`
Solution:
Given,
`(a+2)^2 =(a+2)(a+2)=a(a+2)+2(a+2)=a^2+2a+2a+4=a^2+4a+4.`
The result of the equation is` a^2+4a+4.`
Example 3 for the perfect square formula:
To solve the following `(a-2)^2`
Solution:
Given,
`(a-2)^2 =(a-2)(a-2)=a(a-2)-2(a-2)=a^2-2a-2a+4=a^2-4a+4.`
The result of the equation is` a^2-4a+4.`
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