Question

What is the formula for asquare+bsquare​

Answer 1

Answer:

$a {}^{2} + b {}^{2} = a {}^{2} - 2ab + b {}^{2}$

Explanation:

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Answer 2

$\huge\underline\mathrm{Answer-}$

$\red{\tt{a^2+b^2=(a+b)^2-2ab}}$

A question related to this Identity :

If the whole square of a + b is 10, and the product of a and b is 5, then find the value of a² + b².

Solution :

By using,

$\tt{a^2+b^2=(a+b)^2-2ab}$

putting the given values,

$\implies$ $\tt{a^2+b^2=(10)^2-2(5)}$

$\implies$ $\tt{a^2+b^2=100-10}$

$\implies$ $\tt{a^2+b^2=90}$

Just like this, you can use this Identity.

Some other identities :

★ $\tt{(a+b)^2=a^2+b^2+2ab}$

★ $\tt{(a-b)^2=a^2+b^2-2ab}$

★ $\tt{a^2-b^2=(a+b)(a-b)}$

★ $\tt{(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca}$

★ $\tt{(x+a)(x+b)=x^2+(a+b)x+ab}$