Question

( ax + 6y )^2 -- (6x + ay )^2 = ?​

Answer 1

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FACTORISATION :

${(ax + 6y)}^{2} - {(6x + ay)}^{2}$

a² - b² = ( a + b )( a - b )

$(ax + 6y + 6x + ay)(ax + 6y - 6x - ay)$

SIMPLIFICATION :

${(ax + 6y)}^{2} - {(6x + ay)}^{2}$

(a + b)² = a² + 2ab + b²

$\: \: \: {(ax)}^{2} + 2(ax)(6y) + {(6y)}^{2} \\ - {(6x)}^{2} + 2(6x)(ay) + {(ay)}^{2}$

${a}^{2} {x}^{2} + 12axy + 36 {y}^{2} - (36 {x}^{2} + 12axy + {a}^{2} {y}^{2} )$

${a}^{2} {x}^{2} - {a }^{2} {y}^{2} + 12axy - 12axy + 36 {y}^{2} - 36 {x}^{2}$

${a}^{2} {x}^{2} - {a}^{2} {y}^{2} + 36 {y}^{2} - 36 { x }^{2}$