Algebraic Expressions Exercises 3.2

Today our topic of discussion is Algebraic Expressions Exercises 3.2.

Algebraic Expressions Exercises 3.2

 

 

Exercise 3.2

1. Find the cube with the help of the formulac:

1) 2x² + 3y²

2) 7m² – 2n

3) 2a – b – 3c

2. Simplify:

1) (7x + 3b)³ – (5x + 3b)³- 6x(7x + 3b)(5x + 3b)

2) (a + b + c)³- (a – b – c)³ – 6(b + c)\{a² – (b + c)²\} 3) (m + n) ^ 6 – (m – n) ^ 6 – 12mn * (m² – n ²)²

4) (x + y)(x² – xy + y²) + (y + z)(y² – yz + z²) + (z + x)(z² – zx + x²)

5) (2x + 3y – 4z)³ + (2x – 3y + 4z)³+ 12x\{4x² – (3y – 4z)²}

3. If a – b = 5 and ab = 36 what is the value of a³ 3 – b ³ ?
4. If a ³- b ³= 513 and a – b = 3 what is the value of ab?
5. If x = 19 and y = – 12 , find the value of 8x³ + 36x ² * y + 54x * y ² + 27y ³ .
6. If a = 15 what is the value of 8a³ + 60a ² + 150a +130?
7. If a + b = m , a²+ b ²= n and a ³ + b³ = p ³ , show that, m³ + 2p³ = 3mn .
8. If a + b = 3 and ab = 2 , find the value of (a) * a ² – ab + b² and (b) * a³ + b³

 

 

9. If a – b = 5 and ab = 36 , find the value of (a) a² + ab + b ²and ( b) a³ – b ³ .
10. If m + 1/m = a find the value of m³ + 1/(m ^ 3)
11. If x – 1/x = p find-the value of x³ – 1/(x³)
12. If a – 1/a = 1 show that, a³ – = 4.
13. If a + b + c = 0 , show that,

1) a³+b³+c³ 3abc

2) ((b + c)²)/(3bc) + ((c + a)²)/(3ca) + ((a + b)²)/(3ab) = 1

14. If p – q = r , show that, p³-q3-3=3pqr.
15. If 2x – 2/x = 3 show that, 8(x ³ – 1/(x³)) = 63
16. If a =√6 + √5 , find-the value of
17. x – 1/x = √3 where x ne0

1) Prove that, x² – √3 * x = 1

(a ⁶ – 1)/(a³)

2) Prove that, 23(x² + 1/(x²)) = 5(x ^ 4 + 1/(x ^ 4))

3) Find-the value of x⁶ + 1/(x⁶)

 

 

Read more:

• Classification of Real Numbers
• Newtonian Mechanics