Question:
Factorise each of the following:
(i) 27y 3 + 125z 3
(ii) 64m3 – 343n 3
[ Hint : See Question 9. ]
Factorise each of the following:
(i) 27y 3 + 125z 3
(ii) 64m3 – 343n 3
[ Hint : See Question 9. ]
Updated On: Nov 20, 2023
Hide Solution
Verified By Collegedunia
Solution and Explanation
(i) 27 y3 + 125 z3
= (3y)3 + (5z)3
= (3y + 5z) [(3y)2 + (5z)2 - (3y)(5z) ] [∵ a3 + b3 ]
= (a + b) (a2 + b2 - ab)
= (3y + 5z) [9y2 + 25z2 - 15yz]
(ii) 64m3 - 343n3
= (4m)3 - (7n)3
= (4m - 7n)[ (4m)2 + (7n)2 + (4m) (7n) ] [∵ a3 - b3 = (a - b) (a2 + b2 + 2ab) ]
= (4m - 7n) [16m2 + 49n2 + 28mn ]
Was this answer helpful?
0
0
Top Questions on Algebraic Identities
- The value of \(\frac{a}{(a-b)(a-c)} + \frac{b}{(b-c)(b-a)} + \frac{c}{(c-a)(c-b)}\) is
- JEECUP - 2024
- Mathematics
- Algebraic Identities
- If \(a + b + c = 11\) and \(ab + bc + ca = 20\), then the value of \(a^3 + b^3 + c^3 - 3abc\) is
- JEECUP - 2024
- Mathematics
- Algebraic Identities
- If \( a^4 + \frac{1}{a^4} = 322 \), then the value of \( a - \frac{1}{a} \) is:
- NCHMCT JEE - 2024
- Quantitative Aptitude
- Algebraic Identities
- If 2.5x=0.05 y, then find the value of \((\frac{y-x}{y+x}).\)
- CUET (PG) - 2023
- Mathematics
- Algebraic Identities
- If \( x + \frac{1}{x} = 2 \), then \( x^3 + \frac{1}{x^3} = \)
- CET Delhi Polytechnic - 2018
- Mathematics
- Algebraic Identities
View More Questions
Questions Asked in CBSE Class IX exam
- (i) The kind of person the doctor is (money, possessions)
(ii) The kind of person he wants to be (appearance, ambition)- CBSE Class IX
- The snake and the mirror
- An object of mass 1 kg travelling in a straight line with a velocity of 10 m s–1 collides with, and sticks to, a stationary wooden block of mass 5 kg. Then they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined object.
- CBSE Class IX
- Inertia and Mass
- Fig shows the distance-time graph of three objects A, B and C. Study the graph and answer the following questions:
- Which of the three is travelling the fastest?
- Are all three ever at the same point on the road?
- How far has C travelled when B passes A?
- How far has B travelled by the time it passes C?
- CBSE Class IX
- Graphical Representation of Motion
- A driver of a car travelling at \(52\) \(km \;h^{–1}\) applies the brakes Shade the area on the graph that represents the distance travelled by the car during the period. (b) Which part of the graph represents uniform motion of the car?
- CBSE Class IX
- Graphical Representation of Motion
- Name the following.
- Tissue that forms the inner lining of our mouth.
- Tissue that connects muscle to bone in humans.
- Tissue that transports food in plants.
- Tissue that stores fat in our body.
- Connective tissue with a fluid matrix.
- Tissue present in the brain.
- CBSE Class IX
- Animal Tissues
View More Questions