Question

${a }^{2} + {b }^{2} =$
​

Answer 1

Answer:

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

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

hope this helps (✯ᴗ✯)