Question

write the values of (a+b)²​

Answer 1

Answer:

(a+b)^2 = a^2 +b^2 +2ab

this is the identity

Answer 2

${\huge{\underline{\bf{\pink{Question}}}}}$

write the values of (a+b)²​

${\huge{\boxed{\sf{\green{Answer}}}}}$

The square of this expression is written as ( a − b ) 2 in mathematical form and it is expanded as a 2 − 2 a b + b 2 mathematically. In mathematics, this algebraic identity is used as a formula and it is called in the following three ways. (a-b)²= (a-b)(a-b)

= ${\huge{\underline{\bf{\pink{a(a-b)-b(a-b)}}}}}$ [Addition Distributive Law]

=${\huge{\underline{\bf{\pink{a²-ab-ba+b²}}}}}$ [Addition Distributive Law]

=${\huge{\underline{\bf{\pink{a²-ab-ab+b²}}}}}$ [Multiplication Commutative Law]

=${\huge{\underline{\bf{\pink{a²-2ab+b²}}}}}$

So, ${\huge{\underline{\bf{\pink{(a-b)²= a²-2ab+b²\\}}}}}$

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 “hope this helps!!”

$(a-b)² = (a+b)² - 4ab$

Thanks!