find (a+b)whole sqare +(a-b)whole square using identities
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What is the formula for a²+b²?
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John K Williamsson, Accredited (MS Educ) nerd who loves talking about math
Answered February 22, 2019
There are (at least) two answers to your question, one that you can see (a real answer) and one that you cannot see (an imaginary answer).
Real Answer:
Here is a way that you can use a drawing to remind yourself what a²+b² is equal to in the real world.
Draw a square of a size of your choice, for example 4″ on each side
the size does not matter. Do NOT put size markings (yet).
Decide what arbitrary length along that top and along the side will be a units long. Mark those positions.

Let the remainder of the distance along that side be “b” units.
In other words, each side of the square will be “a+b” un
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Robert Sanford, 9 years of teaching experiences
Answered March 19, 2020
We can say, (a+b)²= (a+b)(a+b)
= a(a+b)+b(a+b) [Addition Distributive Law]
=a²+ab+ba+b² [Addition Distributive Law]
=a²+ab+ab+b² [Multiplication Commutative Law]
=a²+2ab+b²
So (a+b)²= a²+2ab+b²
that is (a+b)² -2ab = a²+2ab+b² -2ab= a²+2ab-2ab+b² = a²+0+b²
= a²+b² [Addition Law of Identity]
So, a²+b²= (a+b)² -2ab
above the same pattern we know
(a-b)²= a²- 2ab+b²
that is (a-b)² +2ab =a²-2ab+b²+2ab= a²-2ab+2ab+b² = a²+0+b²
= a²+b² [Addition Law of Identity]
So,
a²+b²= (a-b)² +2ab
So we can say a²+b²= (a-b)² +2ab
and also
a²+b²= (a+b)² -2ab
Answer:
Hey mate,
Answer to your question is ───
(a + b) ² + (a -b) ²
a² + b² + 2 ab + a² + b² -2ab
2 a² + 2 b²
2 ( a² + b²)