Question

SOLVE .......(a-b)² =❓ ​

Answer 1

(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

Again we know

(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

Now, (a+b)² - 4ab= a²+2ab+b² -4ab= a²+2ab-4ab+b²= a²-2ab+b² = (a-b)²

So, (a-b)² = (a+b)² - 4ab

Finally we can say

(a-b)²= a²-2ab+b²

and also

(a-b)² = (a+b)² - 4ab