Cube

Algebra Level 2

Expand ( a x − b y ) 3 (ax-by)^3 .

a 3 x 3 − 3 a 2 x 2 b y + 3 a x b 2 y 2 − b 3 y 3 a^3x^3 - 3a^2x^2by + 3axb^2y^2 - b^3y^3 a 3 x 2 − 3 a 3 x 3 b y + 3 a x b 2 y 2 − b 3 y a^3x^2 - 3a^3x^3by + 3axb^2y^2 - b^3 y a 3 x 3 − 3 a 2 a 3 x 2 b y + 3 a x b 2 y 2 − b 3 y 3 a^3x^3 - 3a^2a^3x^2by + 3axb^2y^2 - b^3 y^3 a 3 x 3 − b 3 y 3 a^3x^3 - b^3y^3

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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2 solutions

Munem Shahriar
Apr 7, 2017

( a x − b y ) 3 (ax - by)^3

= ( a x ) 3 − 3 × ( a x ) 2 × b y + 3 ⋅ a x ⋅ ( b y ) 2 + ( b y ) 3 = (ax)^3 - 3× (ax)^2 × by + 3 \cdot ax \cdot (by)^2 + (by)^3

= a 3 x 3 − 3 a 2 x 2 b y + 3 a x b 2 y 2 + b 3 y 3 = a^3x^3 - 3 a^2x^2 by + 3 ax b^2y^2 + b^3y^3

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Mohammad Khaza
Jul 21, 2017

(ax - by)³

= (ax)³ - 3× (ax)² × by + 3 × ax × (by)² + (by)³

= a³x³ - 3 a²x² by + 3 ax b²y² + b³y³

so,Ans: a³x³ - 3 a²x² by + 3 ax b²y² + b³y³

the basic formula is= (a-b)³ = a³ - 3a²b + 3ab² + b³

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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