Question

Simplify: (3x – 4y )² + (3x + 4y)²​

Answer 1

Answer:

(3x – 4y )² + (3x + 4y)²​ $= 19 x^2 + 32 y^2$

Step-by-step explanation:

Used following two Formula:

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

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

Simplify: (3x – 4y )² + (3x + 4y)²​

First find value (3x – 4y )²

$(3x - 4y)^2 = (3x)^2 - 2 (3x)(4y) + (4y)^2\\= 9x^2 - 6x(4y) + 16y^2\\= 9x^2 - 24xy + 16y^2$

Then find the value of (3x+ 4y )²

$(3x +4y)^2 = (3x)^2 + 2 (3x)(4y) + (4y)^2\\= 9x^2 +6x(4y) + 16y^2\\= 9x^2 + 24xy + 16y^2$

(3x – 4y )² + (3x + 4y)²​

$= (9x^2 - 24xy + 16y^2)+ (9x^2+ 24xy + 16y^2)\\= 9x^2 - 24xy + 16y^2 + 9x^2+ 24xy + 16y^2$

Rearrange the similar terms

$= 9x^2 - 24xy + 16y^2 + 9x^2+ 24xy + 16y^2 \\= 9x^2 + 9x^2 - 24xy + 24xy + 16y^2 + 16y^2 \\= (9 + 9) x^2 + (16 + 16) y^2 \\= 19 x^2 + 32 y^2$