## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 9 Algebra Ex 9.4

Question 1.

Find the value of the following:

(i) 4^{3}

(ii) (-6)^{4}

(iii) \(\left(\frac{2}{3}\right)^{4}\)

(iv) (-2)^{3} × 5^{2}

Solution:

Question 2.

Find the value of:

(i) 3x + 2y when x = 3 and y – 2

(ii) 5x – 3y when x = 2 and y = -5

(iii) a + 2b – 5c when a = 2, b = -3 and c = 1

(iv) 2p + 3q + 4r + pqr when p = -1, q = 2 and r = 3

(v) 3ab + 4bc – 5ca when a = 4, 6 = 5 and c = -2.

Solution:

Question 3.

Find the value of:

(i) 2x^{2} – 3x + 4 when × = 2

(ii) 4x^{3} – 5x^{2} – 6x + 7 when x = 3

(iii) 3x^{3} + 9x^{2} – x + 8 when x = -2

(iv) 2x^{4} – 5x^{3} + 7x – 3 when x = -3

Solution:

Question 4.

If x = 5, find the value of:

(i) 6 – 7x^{2}

(ii) 3x^{2} + 8x – 10

(iii) 2x^{3} – 4x^{2} – 6x + 25

Solution:

Question 5.

If x = 2, y = 3 and z = -1, find the values of:

(i) x + y

(ii) \(\frac{x y}{z}\)

(iii) \(\frac{2 x+3 y-4 z}{3 x-z}\)

Solution:

Question 6.

If a = 2, b = 3 and c = -2, find the value of a^{2} + b^{2} + c^{2} – 2ab – 2bc – 2ca + 3abc.

Solution:

Question 7.

If p = 4, q = -3 and r = 2, find the value of: p^{3} + q^{3} – r^{3} – 3pqr.

Solution:

Question 8.

If m = 1, n = 2 and p = -3, find the value of 2mn^{4} – 15m^{2}n + p.

Solution:

Question 9.

State true or false:

(i) The value of 3x – 2 is 1 when x = 0.

(ii) The value of 2x^{2} – x – 3 is 0 when x = -1.

(iii) p^{2} + q^{2} – r^{2} when p = 5, q = 12 and r = 13.

(iv) 16 – 3x = 5x when x = 2.

Solution:

Question 10.

For x = 2 and y = -3, verify the following:

(i) (x + y)^{2} = x^{2} + 2xy + y^{2}

(ii) (x – y)^{2} = x^{2} – 2xy + y^{2}

(iii) x^{2} – y^{2} = (x + y) (x – y)

(iv) (x + y)^{2} = (x – y)^{2} + 4xy

(v) (x + y)^{3} = x^{3} + y^{3} + 3x^{2}y + 3xy^{2}

Solution: