Question

the value of 2 X + 3 y whole square + 2 x minus 3 ywhole square is dash

Answer 1

Let 2x = a
Let 3y = b
The given equation is $(2x + 3y) ^{2}$ + $(2x - 3y) ^{2}$
The first term, $(2x + 3y) ^{2}$ is of the form $(a + b) ^{2}$
Similarly, second term is of the form, $(a - b) ^{2}$.
We know that $(a + b) ^{2}$ = $a^{2}$ + 2ab +$b^{2}$.
                      $(a - b) ^{2}$ = $a^{2}$ - 2ab +$b^{2}$.
So, the equation is of the form, $(a + b) ^{2}$ + $(a - b) ^{2}$.

Substitute 2x for "a" and 3y for "b".
We get, $(2x + 3y) ^{2}$ + $(2x - 3y) ^{2}$
             = $(2x)^{2}$ + 2*2x*3y +$(3y)^{2}$ + $(2x)^{2}$ 2*2x*3y +$(3y)^{2}$
            = $4x^{2}$ + 12xy + $9y^{2}$ + $4x^{2}$ - 12xy + $9y^{2}$
            = 2*$4x^{2}$ + 2*$9y^{2}$
            = $8x^{2}$ + $18x^{2}$

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