Question

${x}^{2} + (y}^{2}$
what is the formula?​

Answer 1

$\huge\fbox{\tt{ {x}^{2}+{y}^{2} = {(x+y)}^{2}}}$

This can be expanded into :

$\longrightarrow{\tt{ {x}^{2}+(2\times x \times y)+ {y}^{2}}$

Eg:

$\tt{ {(3+4)}^{2} = {3}^{2} + (2 \times 3 \times 4)+ {4}^{2}}$

$\longrightarrow{\tt { 9+24+16}}$

$\implies{\tt {49}}$

${\tt\pink { verification}}$

3+4 = 7

$\implies{\tt{{7}^{2} = 49}}$

There are more such identities:

• $\implies{\tt\fbox\pink{{(x-y)}^{2}={x}^{2} - (2 \times x \times y) + {y}^{2}}}$
• $\implies{\tt\fbox\pink{(x+y)(x-y) ={x}^{2} - {y}^{2}}}$
• $\implies{\tt\fbox\pink{(x+a)(x+b)={x}^{2} + (a+b)x+ ab}}$