Without actually calculating the cubes, find the value of each of the following:
(i) (–12)3 + (7)3 + (5)3
(ii) (28)3 + (–15)3 + (–13)3
Without actually calculating the cubes, find the value of each of the following:
(i) (–12)3 + (7)3 + (5)3
(ii) (28)3 + (–15)3 + (–13)3
Solution and Explanation
(i) (–12)3 + (7)3 + (5)3
Let x = -12, y = 7, and z = 5
It can be observed that, x + y + z = -12 + 7 + 5 = 0
It is known that if x + y + z = 0, then
x3 + y3 + z3 = 3xyz
∴ (-12)3 + (7)3 + (5)3 = 3(-12) (7) (5) = -1260
(ii) (28)3 + (–15)3 + (–13)3
Let x = 28, y = -15, and z = -13
It can be observed that,
x + y + z = 28 + (-15) + (-13) = 28 - 28 = 0
It is known that if x + y + z = 0,
then x3 + y3 + z3 = 3xyz
∴ (28)3 + (-15)3 + (-13)3 = 3(28) (-15) (-13)=16380
Top Questions on Polynomials in One Variable
Write the degree of each of the following polynomials:
(i) 5x 3 + 4x 2 + 7x (ii) 4 – y 2 (iii) 5t – √7 (iv) 3.
- CBSE Class IX
- Mathematics
- Polynomials in One Variable
- Give one example each of a binomial of degree 35, and of a monomial of degree 100.
- CBSE Class IX
- Mathematics
- Polynomials in One Variable
- Factorise: 27x3+y3+z3–9xy.
- CBSE Class IX
- Mathematics
- Polynomials in One Variable
Write the coefficients of x 2 in each of the following:
(i) 2 + x 2 + x
(ii) 2 – x 2 + x 3
(iii) \(\frac{π }{ 2}\) x2 + x
(iv) √2 x -1
- CBSE Class IX
- Mathematics
- Polynomials in One Variable
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x 2 – 3x + 7
(ii) y 2 + √2
(iii) 3 √t + t√2
(iv) y +\(\frac{ 2 }{ y} \)
(v) x 10 + y 3 + t 50
- Mathematics
- Polynomials in One Variable
Questions Asked in CBSE Class IX exam
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.
Which part of the graph represents uniform motion of the car?- CBSE Class IX
- Graphical Representation of Motion
- Verify : (i) x 3 + y 3 = (x + y) (x 2 – xy + y 2 ) (ii) x 3 – y 3 = (x – y) (x 2 + xy + y 2 ).
- CBSE Class IX
- Algebraic Identities
- 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
- Discuss what these phrases mean to you.
(i) a yellow wood
(ii) it was grassy and wanted wear
(iii) the passing there
(iv) leaves no step had trodden black
(v) how way leads on to way- CBSE Class IX
- The fun they had
- What do you think Dinamani is the name of? Give a reason for your answer.
- CBSE Class IX
- My childhood