Question

$(2x + 3y) {}^{2}$
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Answer 1

Given to find (2x + 3y )²

The question can be solve in Two methods

Method - 1 :-

Applying (a + b )² formula and solving

We know that ( a + b )² = a² + 2ab + b²

(2x + 3y )² Where a = 2x ; b = 3y

(2x + 3y )² = (2x)² + 2 (2x) (3y ) + (3y)²

(2x + 3y )² = 4x² + 12xy + 9y²

So, (2x + 3y )² = 4x² + 12xy + 9y²

Method - 2 :-

(2x + 3y )² can be written as (2x + 3y ) ( 2x + 3y )

Now do the normal multiplication

(2x + 3y ) ( 2x + 3y ) = 2x (2x + 3y) + 3y (2x + 3y)

(2x + 3y ) ( 2x + 3y) = 4x² + 6xy + 6xy + 9y²

(2x + 3y ) ( 2x + 3y) = 4x² + 12xy + 9y²

So,

(2x + 3y)² = 4x² + 12xy + 9y²

______________

Know more Some algebraic identities :-

a+ b)² = a² + b² + 2ab

( a - b )² = a² + b² - 2ab

( a + b )² + ( a - b)² = 2a² + 2b²

( a + b )² - ( a - b)² = 4ab

( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

a² + b² = ( a + b)² - 2ab

(a + b )³ = a³ + b³ + 3ab ( a + b)

( a - b)³ = a³ - b³ - 3ab ( a - b)

If a + b + c = 0 then a³ + b³ + c³ = 3abc

a³ + b³ = ( a + b) (a²-ab + b²)

a³ - b³ = (a -b) (a² + ab + b²)