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(28) 3 + (- 15) 3 + (- 13) 3 . (- 12) 3 + (7) 3 + (5) 3 (- 12) 3 + (7) 3 + (5) 3 = 3(- 12)(7)(5) | ∵ (- 12) + (7) + (5) = 0 = - 1260

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Polynomials

Short Answer Type

211. If x + y + z = 0, show that x³ + y³ + Z³ = 3xyz.

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212. Without actually calculating the cubes, find the value of each of the following:
(- 12)³+ (7)³ + (5)³

(28)³ + (- 15)³ + (- 13)³.
(- 12)³ + (7)³ + (5)³(- 12)³ + (7)³ + (5)³ = 3(- 12)(7)(5)
| ∵ (- 12) + (7) + (5) = 0
= - 1260

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213. Without actually calculating the cubes, find the value of each of the following:
(28)³ + (- 15)³ + (- 13)³

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214. Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:

box enclose bold space bold Area bold space bold colon bold space bold 25 bold a to the power of bold 2 bold minus bold 35 bold a bold plus bold 12 end enclose

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215. Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:

box enclose bold Area bold space bold colon bold space bold 35 bold y to the power of bold 2 bold plus bold 13 bold y bold minus bold 12 end enclose

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216.

What are the possible expressions for the dimensions of the cuboids whose volumes are given below?

$box enclose bold Volume bold space bold colon bold space bold 3 bold x to the power of bold 2 bold minus bold 12 bold x end enclose$

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217.

What are the possible expressions for the dimensions of the cuboids whose volumes are given below?

$box enclose bold Volume bold space bold colon bold space bold 12 bold ky to the power of bold 2 bold plus bold 8 bold ky bold minus bold 20 bold k end enclose$