Question

simplify (4x+9y)^2+(4x-9y)^2​

Answer 1

$(4 {x}^{2} + 9 {y}^{2} ) + (4 {x}^{2} - 9 {y}^{2} ) \\ \\ using \: formula = > \\ \\ = 16 {x}^{2} + 81 {y}^{2} + 72xy \\ + 16 {x}^{2} + 81 {y}^{2} - 72xy \\ = 32 {x}^{2} + 162 {y}^{2} \\ \\ now \: put \: values \: of \: x \: and \: y \: and \: u \: can \: solve \: futher \: like \: this$

Answer 2

a^2 + b^2 = (a + b)^2 - 2*a*b —> 1

Given:

(4x + 9y)^2 + (4x - 9y)^2

Let

a = 4x + 9y

b = 4x - 9y

Substitute a & b in 1, we get

(4x + 9y)^2 + (4x - 9y)^2

= (4x + 9y + 4x - 9y)^2 - 2*(4x + 9y)*(4x - 9y)

= (8x)^2 - 2*(4x + 9y)*(4x - 9y)

= 64x^2 - 2*(16x^2 - 81y^2)

[using (a + b)*(a - b) = a^2 - b^2]

= 64x^2 - 32x^2 + 162y^2

= 32x^2 + 162y^2 ——> Answer