Question
Factorise:
(3a - 2b)3 + (2b - 5c)3 + (5c - 3a)3
(3a - 2b)3 + (2b - 5c)3 + (5c - 3a)3
✓
Answer
Put (3a - 2b) = x, (2b - 5c) = y and (5c - 3a) = z.
We have:
x + y + z = 3a - 2b + 2b - 5c + 5c - 3a = 0
Now,
(3a - 2b)3 + (2b - 5c)3 + (5c - 3a)3 = x3 + y3 + z3
= 3xyz [Here, x + y + z = 0. So, x3 + y3 + z3]
= (3a - 2b)(2b - 5c)(5c - 3a)
We have:
x + y + z = 3a - 2b + 2b - 5c + 5c - 3a = 0
Now,
(3a - 2b)3 + (2b - 5c)3 + (5c - 3a)3 = x3 + y3 + z3
= 3xyz [Here, x + y + z = 0. So, x3 + y3 + z3]
= (3a - 2b)(2b - 5c)(5c - 3a)
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
Simplify:
$\Bigg(\frac{15^\frac{1}{3}}{9^\frac{1}{4}}\Bigg)^{-6}$
→$\Bigg(\frac{15^\frac{1}{3}}{9^\frac{1}{4}}\Bigg)^{-6}$
Simplify:
$(0.001)^{\frac{1}{3}}$
→$(0.001)^{\frac{1}{3}}$
Evaluate the following using identities:
(0.98)2
(0.98)2
Express the following equation in the form ax + by + c = 0 and indicate the values of a, b, c in case.
4y = 7
4y = 7
LM is a line parallel to the y-axis at a distance of 3 units:
- What are the coordinates of the points P, R and Q?
- What is the difference between the abscissa of the points L and M?
The mean of 31 results is 60. If the mean of the first 16 results is 58 and that of the last 16 results is 62, find the 16th result.
Factorize:
64a3 + 125b3 + 240a2b + 300ab2
64a3 + 125b3 + 240a2b + 300ab2
Write the reciprocal of $\big(2+\sqrt{3}\big).$
→Arun scored 36 marks in English, 44 marks in Hindi, 75 marks in mathematics and x marks in science. If he has secured an average of 50 marks, find the value of x.
Find the following products:
$\Big(\frac{3}{\text{x}}-\frac{5}{\text{y}}\Big)\Big(\frac{9}{\text{x}^2}+\frac{25}{\text{y}^2}+\frac{15}{\text{xy}}\Big)$
→$\Big(\frac{3}{\text{x}}-\frac{5}{\text{y}}\Big)\Big(\frac{9}{\text{x}^2}+\frac{25}{\text{y}^2}+\frac{15}{\text{xy}}\Big)$