A Square Plus B Square Formula


To calculate the sum of two or more squares in an expression, the a^2 + b^2 formula is used. The a2 + b2 formula can be easily derived using the (a+b)2or(a-b)2 formula. Let us learn these along with a few solved examples in the upcoming sections.

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What Is the a^2 + b^2 Formula?

Thea^2 + b^2 formula is usedto calculate the sum of two or more squares in an expression. Thus, a sum of squares formula ora^2 + b^2 formulacan be expressed as:

a2+ b2= (a +b)2- 2ab

Also,a2+ b2= (a - b)2+2abwhere, a, b = arbitrary numbers.


Let a & b be the twonumbers, the squares of a and b area2and b2. The sum of the squares of a & b isa2+ b2. We could obtain a formula using the knownalgebraic identity(a+b)2= a2+ b2+ 2ab. On subtracting 2abfrom both the sides we can conclude thata2+ b2= (a +b)2- 2ab.

Similarly, we can also say that,a2+ b2= (a - b)2+2ab.

Let us have a look at a few solved examples on the a^2 + b^2formula lớn understand the concept better.


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Example on a^2 + b^2 Formula

Example 1: Using sum of squares formula, find the value of 52 + 62?


To find : value of 52 + 62Given: a = 5, b = 6Using sum of squares Formula,a2 + b2 = (a + b)2 − 2ab52 + 62 = (5 + 6)2 − 2(5)(6)= 121 − 2(30)= 121− 60= 61

Answer: The value of 52 + 62is61.

Example 2 :Verifythat the value of x2 + y2 is(x + y)2- 2xy usinga2+ b2formula.

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Solution:To verifyx2 + y2 =(x + y)2- 2xyLet us use thea2+ b2formulaa = x, b = yUsing the (a + b)2 formula let us expand the initial terms.(a + b)2= a2 + b2 + 2abLet us substitute the value of a and b as x & y(x + y)2= x2 + y2 + 2xyOn subtracting 2xy from both the sides,x2 + y2=(x + y)2- 2xy

Answer: Hence verified

Example 3: Find the sum of the squares of 10 & 20 directly & using thea^2 + b^2 formula. Verify your answers.Solution:102+ 202= 100 + 400 = 500Using the formulaa2+ b2= (a +b)2-2ab, we get102+ 202= (10 + 20)2- 2× 10× 20= 900- 400= 500Thus verified.

FAQs on a2+ b2Formula

What Is the Expansion of a2+ b2Formula?

a2+b2formula is known as the sum of squares formula it is read as a square plus b square. Its expansion is expressed asa2+ b2= (a + b)2-2ab.

What Is thea2+ b2 Formula in Algebra?

The a2+ b2 formula is one of the important algebraic identities. It is represented bya2 + b2and is read as a square plus b square. The (a2+b2) formula is expressed asa2+ b2= (a +b)2-2ab.

How khổng lồ Simplify Numbers Usingthea2+ b2 Formula?

Let us understand the use of the a2+ b2 a2+b2formula with the help of the following example.Example: Find the value of 202+ 302using the a2+ b2formula.To find:202+302Let us assume that a = 20 and b = 30.We will substitute these in the formula of the sum of squares formula that is, a2+ b2a2+ b2= (a +b)2-2ab202+302= (20+30)2- 2(20)(30)= 2500- 1200 = 1300Answer:202+302= 1300.

How to Use the a2+ b2 Formula Give Steps?

The following steps are followed while using the a2+ b2formula.

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Firstlyobserve the pattern of the two numbers whether thenumbers have ^2 as power or not and in the khung of a2+ b2.Write down the sum of squares formula ofa2+ b2= (a +b)2-2abSubstitute the value ofa and b in the sum of squares a2+ b2 formula & simplify.