Question
Factorise:
27x3 - y3 - z3 - 9xyz
27x3 - y3 - z3 - 9xyz
✓
Answer
27x3 - y3 - z3 - 9xyz
= (3x)3 - y3 - z3 - 3 × (3x) × (-y) × (-z)
We know,
a3 + b3 + c3 - 3abc
= (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
a = 3x, b = -y, c = -z
(3x)3 - y3 - z3 - 3 × (3x) × (-y) × (-z)
= (3x - y - z)(9x2 + y2 + z2 + 3xy - yz + 3xz)
= (3x)3 - y3 - z3 - 3 × (3x) × (-y) × (-z)
We know,
a3 + b3 + c3 - 3abc
= (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
a = 3x, b = -y, c = -z
(3x)3 - y3 - z3 - 3 × (3x) × (-y) × (-z)
= (3x - y - z)(9x2 + y2 + z2 + 3xy - yz + 3xz)
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
30 children were asked about the number of hours they watched TV programmes last week. The results are recorded as under:
Can we say that the number of children who watched TV for 10 or more hours a week is 22? Justify your answer.
| Number of hours | 0-5 | 5-10 | 10-15 | 15-20 |
| Frequency | 8 | 16 | 4 | 2 |
The mean of the markes scored by 50 students was found to be 39. Later on it was discoverd that a score of 43 was misread as 23. Find the correct mean.
Multiply:
(x2 + y2 + z2 - xy + xz + yz) by (x + y -z)
(x2 + y2 + z2 - xy + xz + yz) by (x + y -z)
Give possible expressions for the length and breadth of the rectangle whose area is given by 4a2 + 4a - 3.
A forest ranger keeps track of bears in his area. He plotted their location on a graph. The origin represents the ranger's control room’s location. To access and maintain equipment, Road x and Road yhave been laid and paved inside the forest. They pass through the control room.
One unit on the graph paper represents 1 km.
1. Which bear is nearest to a paved road?
2. Bear 467 has been injured. The forest rescue team starts from the control room and decides to use the paved road as much as possible. Which road should they take?
One unit on the graph paper represents 1 km.
1. Which bear is nearest to a paved road?
2. Bear 467 has been injured. The forest rescue team starts from the control room and decides to use the paved road as much as possible. Which road should they take?
Factorise:
9a2 + 6a + 1 - 36b2
9a2 + 6a + 1 - 36b2
Express the following rational numbers as decimals:
$\frac{42}{100}$
→$\frac{42}{100}$
Show that 0.2353535... = $0. 2\overline{35}$, can be expressed in the form $\frac{p}{q}$, where p and q are integers and q $\ne$ 0.
→Simplify:
$\Big(\frac{32}{243}\Big)^{-\frac{4}{5}}$
→$\Big(\frac{32}{243}\Big)^{-\frac{4}{5}}$
Find the total surface area of a cone, if its slant height is 21m and diameter of its base is 24m. $\Big(\text{Use}\ \pi=\frac{22}{7}\Big).$
→