Factorize each of the following expressions:
8x³-125y³+180xy+216
Answers
The algebraic expression is given as : 8x³ - 125y³ + 180xy + 216
We can rewrite the given expression as :
(2x)³ + (- 5y)³ + (6)³ − 3(2x)(-5y)(6)
We know, a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c²− ab − bc − ca)
= (2x - 5y + 6)){ (2x)² +(-5y)² + (6)² −2x × -5y − (-5y) (6) −(6)2x}
= (2x + 3y − 6z) {4x² + 25y² + 36 +10xy + 30y - 12x}
8x³ - 125y³ + 180xy + 216 = (2x + 3y − 6z) {4x² + 25y² + 36 +10xy + 30y - 12x}
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Answer:
Step-by-step explanation:
We know, a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c²− ab − bc − ca)
= (2x - 5y + 6)){ (2x)² +(-5y)² + (6)² −2x × -5y − (-5y) (6) −(6)2x}
= (2x + 3y − 6z) {4x² + 25y² + 36 +10xy + 30y - 12x}
8x³ - 125y³ + 180xy + 216 = (2x + 3y − 6z) {4x² + 25y² + 36 +10xy + 30y - 12x}