ICSE

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Ex 10.4

Question 1.
Divide:
(i) – 39pq²r⁵ by – 24p³q³r
(ii) –\(\frac{3}{4}\)a²b³ by \(\frac{6}{7}\)a³b²
Solution:

Question 2.
Divide:
(i) 9x⁴ – 8x³ – 12x + 3 by 3x
(ii) 14p²q³ – 32p³q² + 15pq² – 22p + 18q by – 2p²q.
Solution:

Question 3.
Divide:
(i) 6x² + 13x + 5 by 2x + 1
(ii) 1 + y³ by 1 + y
(iii) 5 + x – 2x² by x + 1
(iv) x³ – 6x² + 12x – 8 by x – 2
Solution:

Question 4.
Divide:
(i) 6x³ + x² – 26x – 25 by 3x – 7
(ii) m³ – 6m² + 7 by m – 1
Solution:

Question 5.
Divide:
(i) a³ + 2a² + 2a + 1 by + a² + a + 1
(ii) 12x³ – 17x² + 26x – 18 by 3x² – 2x + 5
Solution:

Question 6.
If the area of a rectangle is 8x² – 45y² + 18xy and one of its sides is 4x + 15y, find the length of the adjacent side.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Ex 10.3

Question 1.
Multiply:
(i) (5x – 2) by (3x + 4)
(ii) (ax + b) by (cx + d)
(iii) (4p – 7) by (2 – 3p)
(iv) (2x² + 3) by (3x – 5)
(v) (1.5a – 2.5b) by (1.5a + 2.56)
(vi) \(\left(\frac{3}{7} p^{2}+4 q^{2}\right) \text { by } 7\left(p^{2}-\frac{3}{4} q^{2}\right)\)
Solution:

Question 2.
Multiply:
(i) (x – 2y + 3) by (x + 2y)
(ii) (3 – 5x + 2 × 2) by (4x – 5)
Solution:

Question 3.
Multiply:
(i) (3x² – 2x – 1) by (2x² + x – 5)
(ii) (2 – 3y – 5y²) by (2y – 1 + 3y²)
Solution:

Question 4.
Simplify:
(i) (x² + 3) (x – 3) + 9
(ii) (x + 3) (x – 3) (x + 4) (x – 4)
(iii) (x + 5) (x + 6) (x + 7)
(iv) (p + q – 2r) (2p – q + r) – 4qr
(v) (p + q) (r + s) + (p – q)(r – s) – 2(pr + qs)
(vi) (x + y + z) (x – y + z) + (x + y – z) (-x + y + z) – 4zx
Solution:

Question 5.
If two adjacent sides of a rectangle are 5x² + 25xy + 4y² and 2x² – 2xy + 3y², find its area.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Ex 10.2

Question 1.
Find the product of:
(i) 4x³ and -3xy
(ii) 2xyz and 0
(iii) –\(\frac{2}{3}\)p²q, \(\frac{3}{4}\)pq² and 5pqr
(iv) -7ab,-3a³ and –\(\frac{2}{7}\)ab²
(v) –\(\frac{1}{2}\)x² – \(\frac{3}{5}\)xy, \(\frac{2}{3}\)yz and \(\frac{5}{7}\)xyz
Solution:

Question 2.
Multiply:
(i) (3x – 5y + 7z) by – 3xyz
(ii) (2p² – 3pq + 5q² + 5) by – 2pq
(iii) (\(\frac{2}{3}\)a²b – \(\frac{4}{5}\)ab² + \(\frac{2}{7}\)ab + 3) by 35ab
(iv) (4x² – 10xy + 7y² – 8x + 4y + 3) by 3xy
Solution:

Question 3.
Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively:
(i) (p²q, pq²)
(ii) (5xy, 7xy²)
Solution:

Question 4.
Find the volume of rectangular boxes with the following length, breadth and height respectively:
(i) 5ab, 3a²b, 7a⁴b²
(ii) 2pq, 4q², 8rp
Solution:

Question 5.
Simplify the following expressions and evaluate them as directed:
(i) x²(3 – 2x + x²) for x = 1; x = -1; x = \(\frac{2}{3}\) and x = –\(\frac{1}{2}\)
(ii) 5xy(3x + 4y – 7) – 3y(xy – x² + 9) – 8 for x = 2, y = -1
Solution:

Question 6.
Add the following:
(i) 4p(2 – p²) and 8p³ – 3p
(ii) 7xy(8x + 2y – 3) and 4xy²(3y – 7x + 8)
Solution:

Question 7.
Subtract:
(i) 6x(x – y + z)- 3y(x + y – z) from 2z(-x + y + z)
(ii) 7xy(x² -2xy + 3y²) – 8x(x²y – 4xy + 7xy²) from 3y(4x²y – 5xy + 8xy²)
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Ex 10.1

Question 1.
Identify the terms, their numerical as well as literal coefficients in each of the following expressions:
(i) 12x²yz – 4xy²
(ii) 8 + mn + nl – lm
Solution:

Question 2.
Identify monomials, binomials, and trinomials from the following algebraic expressions :
(i) 5p × q × r²
(ii) 3x² + y ÷ 2z
(iii) -3 + 7x²
(iv) \(\frac{5 a^{2}-3 b^{2}+c}{2}\)
(v) 7x⁵ – \(\frac{3 x}{y}\)
(vi) 5p ÷ 3q – 3p² × q²
Solution:

Question 3.
Identify which of the following expressions are polynomials. If so, write their degrees.
(i) \(\frac{2}{5}\)x⁴ – \(\sqrt{3}\)x² + 5x – 1
(ii) 7x³ – \(\frac{3}{x^{2}}\) + \(\sqrt{5}\)
(iii) 4a³b² – 3ab⁴ + 5ab + \(\frac{2}{3}\)
(iv) 2x²y – \(\frac{3}{x y}\) + 5y³ + \(\sqrt{3}\)
Solution:

Question 4.
Add the following expressions:
(i) ab – bv, bv – ca, ca – ab
(ii) 5p²q² + 4pq + 7,3 + 9pq – 2p²q
(iii) l² + m² + n², lm + mn, mn + nl, nl + lm
(iv) 4x³ – 7x² + 9, 3x² – 5x + 4, 7x³ – 11x + 1, 6x² – 13x
Solution:

Question 5.
Subtract:
(i) 8a + 3ab – 2b + 7 from 14a – 5ab + 7b – 5
(ii) 8xy + 4yz + 5zx from 12xy – 3yz – 4zx + 5xyz
(iii) 4p²q – 3pq + 5pq² – 8p + 7q -10 from 18 – 3p – 11q + 5pq – 2pq² + 5p²q
Solution:

Question 6.
Subtract the sum of 3x² + 5xy + 7y² + 3 and 2x² – 4xy – 3y² + 7 from 9x² – 8xy + 11y²
Solution:

Question 7.
What must be subtracted from 3a² – 5ab – 2b² – 3 to get 5a² – 7ab – 3b² + 3a ?
Solution:

Question 8.
The perimeter of a triangle is 7p² – 5p + 11 and two of its sides are p² + 2p – 1 and 3p² – 6p + 3. Find the third side of the triangle.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 9 Direct and Inverse Variation Check Your Progress

Question 1.
Match each of the entries in column I with the appropriate entry in column II.

Solution:

Question 2.
(i) From the following table, determines and q if x and y vary directly:

(ii) From the following table, determine a and b if x and y vary inversely:

Solution:

Question 3.
It rained 80 mm in the first 20 days of April. What would be the total rainfall in April?
Solution:

Question 4.
Mamta earns ₹540 for a working week of 48 hours. If she was absent for 6 hours, how much did she earn?
Solution:

Question 5.
Navjot can do a piece of work in 6 days working 10 hours per day. In how many days can he do the same work if he increases his working hours by 2 hours per day?
Solution:

Question 6.
Sharmila has enough money to buy 24 bananas at the rate of ₹ 1·50 per banana. How many bananas she can buy if the price of each orange is decreased by 30 paise?
Solution:

Question 7.
A fort has rations for 180 soldiers for 40 days. After 10 days, 30 soldiers leave the fort. Find the total number of days for which the food will last.
Solution:

Question 8.
There are 100 students in a hostel. Food provision for them is for 20 days. How long will these provisions last, if 25 more students join the group?
Solution:

Question 9.
If 4 goats or 6 sheep can graze a field in 40 days, how many days will 4 goats and 14 sheep take to graze the same field?
Solution:

Question 10.
A tap can fill a tank in 20 hours, while the other can empty it in 30 hours. The tank is empty and if both taps are opened together, how long will it take for the tank to be half full?
Solution:

Question 11.
Three ants separately can gobble a grasshopper in 3,4, and 6 days respectively. How many days will they take together to finish off the poor chap? If the grasshopper weighs 63 gram, find the share of each.
Solution:

Question 12.
A and B together can do a piece of work in 12 days; B and C together can do it in 15 days. If A is twice as good a workman as C, in how many days A alone will do the same work?
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths