Question
Simplify :
(3a + 5b)³ – (3a – 5b)³
✓
Answer
(3a + 5b)³ – (3a – 5b)³
Here, A = 3a + 5b and B = 3a – 5b
= [(3a + 5b) – (3a – 5b)] [(3a + 5b)² + (3a + 5b) (3a – 5b) + (3a – 5b)²]
…[∵ A³ – B³ = (A – B)(A² + AB + B²)]
= (3a + 5b – 3a + 5b) [(9a² + 30ab + 25b²) + (9a² – 25b²) + (9a² – 30ab + 25b²)]
= 10b (9a² + 9a² + 9a² + 30ab – 30ab + 25b² – 25b² + 25b²)
= 10b (27a² + 25b²)
= 270a²b + 250b³
Here, A = 3a + 5b and B = 3a – 5b
= [(3a + 5b) – (3a – 5b)] [(3a + 5b)² + (3a + 5b) (3a – 5b) + (3a – 5b)²]
…[∵ A³ – B³ = (A – B)(A² + AB + B²)]
= (3a + 5b – 3a + 5b) [(9a² + 30ab + 25b²) + (9a² – 25b²) + (9a² – 30ab + 25b²)]
= 10b (9a² + 9a² + 9a² + 30ab – 30ab + 25b² – 25b² + 25b²)
= 10b (27a² + 25b²)
= 270a²b + 250b³
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
A village, having a population of 4000 requires 150 litres water per head per day. It has a tank which is 20m long, 15m broad and 6m high. For how many days the water of this tank will last?
A cylindrical water tank of diameter 1.4m and height 2.1m is being fed by a pipe of diameter 3.5cm through which water flows at the rate of 2 metre per second. In how much time the tank will be filled?
The difference between the compound interest and the simple interest on a certain sum for 2 years at 6% per annum is Rs. 90. Find the sum.
A and B can finish a piece of work in 16 days and 12 days respectively. A started the work and worked at it for 2 days. He was then joined by B. Finish the total time taken to finish the work.
A cellphone was marked at 40% above the cost price and a discount of 30% was given on its marked price. Find the gain or loss percent made by the shopkeeper.
Solve:
$\frac{\text{2x}+7}{5}-\frac{\text{3x}+11}{2}=\frac{2\text{x}+8}{3}-5$
→$\frac{\text{2x}+7}{5}-\frac{\text{3x}+11}{2}=\frac{2\text{x}+8}{3}-5$
Verify the following:
$\Big(\frac{-7}{11}+\frac{2}{-5}\Big)+\frac{-13}{22}=\frac{-7}{11}+\Big(\frac{2}{-5}+\frac{-13}{22}\Big)$
→$\Big(\frac{-7}{11}+\frac{2}{-5}\Big)+\frac{-13}{22}=\frac{-7}{11}+\Big(\frac{2}{-5}+\frac{-13}{22}\Big)$
Find the area of Fig. as the sum of the areas of two trapezium and a rectangle.
Factorize :
y² + 24y + 144
The diagonal of a quadrilateral shaped field is 24m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13m. Find the area of the field.