what does a square + b square

Step 1: Understand the terms

The term $a^2$ means 'a squared', which is the product of 'a' multiplied by itself. Similarly, $b^2$ means 'b squared', which is 'b' multiplied by itself.

Step 2: Interpret the expression

The expression $a^2 + b^2$ represents the sum of the square of 'a' and the square of 'b'. It is a fundamental algebraic expression.

Step 3: Recognize common applications

This expression is famously known from the Pythagorean theorem, where in a right-angled triangle, the square of the hypotenuse ($c^2$) is equal to the sum of the squares of the other two sides ($a^2 + b^2$). It also appears in the distance formula and the expansion of $(a+b)^2$ or $(a-b)^2$.

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