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1.
Factorise each of the following:
(ii) $64m^3 – 343n^3$
[Hint : See Question 9.]
2.
Factorise : $27x^3 + y^3 + z^3 – 9xyz$
3.
Verify that $x^3 + y^3 + z^3 – 3xyz = \frac{1}{2}(x + y + z)[(x – y)^2 + (y – z)^2 + (z – x)^2]$
4.
If $x + y + z = 0$, show that $x^3 + y^3 + z^3 = 3xyz$.
5.
Without actually calculating the cubes, find the value of each of the following:
(i) $(–12)^3 + (7)^3 + (5)^3$
6.
Without actually calculating the cubes, find the value of each of the following:
(ii) $(28)^3 + (–15)^3 + (–13)^3$
7.
Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:
(i) Area : $25a^2 – 35a + 12$
8.
Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:
(ii) Area : $35y^2 + 13y –12$
9.
What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
(i) Volume : $3x^2 – 12x$
10.
What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
(ii) Volume : $12ky^2 + 8ky – 20k$
- OR -

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