Question
Factorise: $\mathrm{x}^3+64 \mathrm{y}^3$
✓
Answer
x³ + 64y³
= x³ + (4y)³
Here, a = x and b = 4y
∴ x³ + 64y³ = (x + 4y) [x² – x(4y) + (4y)²]
….[∵ a³ + b³ = (a + b)(a² – ab + b²)]
= (x + 4y)(x² – 4xy + 16y²)
= x³ + (4y)³
Here, a = x and b = 4y
∴ x³ + 64y³ = (x + 4y) [x² – x(4y) + (4y)²]
….[∵ a³ + b³ = (a + b)(a² – ab + b²)]
= (x + 4y)(x² – 4xy + 16y²)
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
The population of a suburb is 16,000. Find the rate of increase in the population if the population after two years is 17,640.
A group of 3 friends staying together, consume 54kg of wheat every month. Some more friends join this group and they find that the same amount of wheat lasts for 18 days. How many new members are there in this group now?
Find the surface area of a cuboid whose:
Length $=6 dm$, breadth $=8 dm$, height $=10 dm$.
→Length $=6 dm$, breadth $=8 dm$, height $=10 dm$.
Top surface of a table is trapezium in shape. Find its area if its parallel sides are 1m and 1.2m and perpendicular distance between them is 0.8m.
Evaluate:
$\sqrt[3]{36}\times\sqrt[3]{384}$
→$\sqrt[3]{36}\times\sqrt[3]{384}$
The sum of the radius of the base and height of a solid cylinder is 37 m . If the total surface area of the solid cylinder is $1628 m^2$, find the circumference of its base.
→Find the least square number, exactly divisible by one of the numbers:
6, 9, 15 and 20
6, 9, 15 and 20
55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days?
The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the measure of each of these angles.
Find the square root of the following correct to three places of decimal:
17
17