The polynomial 64x3 + y3 − 8z3 + 24xyz can be expressed in the factor form as (4x + y − 2z)(_____) .

8x 2 + y 2 + 2 z 2 − 2 xy + yz + 4 xz

8x 2 + y 2 + 2 z 2 − 2 xy + yz + 4 xz

16 x 2 + y 2 + 4 z 2 − 4 xy + 2 yz + 8 xz

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The polynomial 64x³ + y³ − 8z³ + 24xyz can be expressed in the factor form as (4x + y − 2z)(_____) .

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8x² + y² + 2z² − 2xy + yz + 4xz

16x² + y² + 4z² − 4xy + 2yz + 8xz

16x² + y² + 4z²

4xy + 2yz + 8xz

answer is A.

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The given polynomial is 64x³ + y³ − 8z³ + 24xyz.

64x³ + y³ − 8z³ + 24xyz

= (4x)³ + (y)³ + (−2z)³ − 3(4x)(y)(−2z), which is of the form a³ + b³ + c³ − 3abc, where a = 4x, b = y, and c = −2z.

We know that,

a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)

∴ 64x³ + y³ − 8z³ + 24xyz

= (4x)³ + (y)³ + (−2z)³ − 3(4x)(y)(−2z)

= (4x + y − 2z)(16x² + y² + 4z² − 4xy + 2yz + 8xz)

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