Question
Factorise:
$8\text{x}^3-\frac{1}{27\text{y}^3}$
$8\text{x}^3-\frac{1}{27\text{y}^3}$
✓
Answer
We know that:
Since a3 - b3 = (a - b)(a2 + a × b + b2)
Let us rewrite
$8\text{x}^3-\frac{1}{27\text{y}^3}$
$=(2\text{x})^3-\Big(\frac{1}{3\text{y}}\Big)^3$
$=\Big(2\text{x}-\frac{1}{3\text{y}}\Big)\bigg[(2\text{x})^2+2\text{x}\times\frac{1}{3\text{y}}+\Big(\frac{1}{3\text{y}}\Big)^2\bigg]$
$=\Big(2\text{x}-\frac{1}{3\text{y}}\Big)\Big(4\text{x}^2+\frac{2\text{x}}{3\text{y}}+\frac{1}{9\text{y}^2}\Big)$
Since a3 - b3 = (a - b)(a2 + a × b + b2)
Let us rewrite
$8\text{x}^3-\frac{1}{27\text{y}^3}$
$=(2\text{x})^3-\Big(\frac{1}{3\text{y}}\Big)^3$
$=\Big(2\text{x}-\frac{1}{3\text{y}}\Big)\bigg[(2\text{x})^2+2\text{x}\times\frac{1}{3\text{y}}+\Big(\frac{1}{3\text{y}}\Big)^2\bigg]$
$=\Big(2\text{x}-\frac{1}{3\text{y}}\Big)\Big(4\text{x}^2+\frac{2\text{x}}{3\text{y}}+\frac{1}{9\text{y}^2}\Big)$
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Read the Source/ Text given below and answer these questions:
Roshan decorated one of his bathroom wall with tiles as shown in the picture. He was having tiles of four colours orange, yellow, green and blue. He fitted the tiles in 8 columns and 12 rows. The size of one tile was 1 foot × 1 foot and the area of each tile is 1 foot2. He arranged the tile in such a way that colour of tiles in each row and column were in the pattern: Orange → Yellow → green → Blue → Orange → ..... and so on.
questions:
1. Which colour tile was fitted at the point with coordinate (2, 5)?
2. What is the area of the tiles fitted in the rectangular part OABX?
Roshan decorated one of his bathroom wall with tiles as shown in the picture. He was having tiles of four colours orange, yellow, green and blue. He fitted the tiles in 8 columns and 12 rows. The size of one tile was 1 foot × 1 foot and the area of each tile is 1 foot2. He arranged the tile in such a way that colour of tiles in each row and column were in the pattern: Orange → Yellow → green → Blue → Orange → ..... and so on.
questions:
1. Which colour tile was fitted at the point with coordinate (2, 5)?
2. What is the area of the tiles fitted in the rectangular part OABX?