Tamilnadu State Board New Syllabus Samacheer Kalvi 8th Maths Guide Pdf Chapter 3 Algebra Ex 3.2 Text Book Back Questions and Answers, Notes.

   

Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 3 Algebra Ex 3.2

Question 1.
Fill in the blanks
(i)

Samacheer Kalvi 8th Maths Guide Answers Chapter 3 Algebra Ex 3.2 1
Answer:
\(\frac{18 m^{4}\left(n^{8}\right)}{2 m^{(3)} n^{3}}\) = 9 mn5

Samacheer Kalvi 8th Maths Guide Chapter 3 Algebra Ex 3.2

(ii)
Samacheer Kalvi 8th Maths Guide Answers Chapter 3 Algebra Ex 3.2 2
Answer:
\(\frac{l^{4} m^{5} n^{(7)}}{2 l m^{(3)} n^{6}}=\frac{l^{3} m^{2} n}{2}\)

(iii)
Samacheer Kalvi 8th Maths Guide Answers Chapter 3 Algebra Ex 3.2 3
Answer:
\(\frac{42 a^{4} b^{5}\left(c^{2}\right)}{6(a)^{4}(b)^{2}}\) = (7)b3c2

Question 2.
Say True or False
(i) 8x3y ÷ 4x2 = 2xy
Answer:
True

Samacheer Kalvi 8th Maths Guide Chapter 3 Algebra Ex 3.2

(ii) 7ab3 ÷ 14 ab = 2b2
Answer:
False

Question 3.
Divide
(i) 27 y3 by 3y
(ii) x3 y2 by x2y
(iii) 45x3 y2 z4 by (-15 xyz)
(iv) (3xy)2 by 9xy
Answer:
(i) 27 y3 by 3y
\(\frac{27 y^{3}}{3 y}\) = \(\frac{27}{3} y^{3-1}\) = 9y2

(ii) x3 y2 by x2y
\(\frac{x^{3} y^{2}}{x^{2} y}\) = x3-2 y2-1 = x1 y1 = xy

(iii) 45x3 y2 z4 by (-15 xyz)
\(\frac{45 x^{3} y^{2} z^{4}}{-15 x y z}\) = \(\frac{45}{-15}\) x3-2 y2-1 y4-1 z4-1 = -3x2 yz3

Samacheer Kalvi 8th Maths Guide Chapter 3 Algebra Ex 3.2

(iv) (3xy)2 by 9xy
\(\frac{(3 x y)^{2}}{3 \times(3 x y)}\) = \(\frac{(3 x y)^{2}}{3 \times(3 x y)}\) = \(\frac{1}{3}\) (3xy)2-1 = \(\frac{1}{3}\) 3xy = xy

Question 4.
Simplify
(i) \(\frac{3 m^{2}}{m}+\frac{2 m^{4}}{m^{3}}\)
(ii) \(\frac{14 p^{5} q^{3}}{2 p^{2} q} \frac{12 p^{3} q^{4}}{3 q^{2}}\)
Answer:
(i) \(\frac{3 m^{2}}{m}+\frac{2 m^{4}}{m^{3}}\)
\(\frac{3 m^{2}}{m}+\frac{2 m^{4}}{m^{3}}\) = 3m2-1 + 2m4-3
= 3m + 2m
= (3 + 2) m
= 5m

(ii) \(\frac{14 p^{5} q^{3}}{2 p^{2} q} \frac{12 p^{3} q^{4}}{3 q^{2}}\)
\(\frac{14 p^{5} q^{3}}{2 p^{2} q} \frac{12 p^{3} q^{4}}{3 q^{2}}\) = \(\frac{14}{2}\)p5-2q3-1 – \(\frac{12}{3}\) p3q4-3
= 7p3q2 – 4p3q

Samacheer Kalvi 8th Maths Guide Chapter 3 Algebra Ex 3.2

Question 5.
Divide:
(i) 32y2 – 8yz by 2y
(ii) (4m2n3 + 16m4 n2 – mn) by 2mn
(iii) 5xy2 – 18x2y3 + 6xy by 6xy
(iv) 81(p4 q2 r3 + 2p3q3 r2 – 5p2q2r2) by (3pqr)2
Answer:
(i) 32y2 – 8yz by 2y
Samacheer Kalvi 8th Maths Guide Answers Chapter 3 Algebra Ex 3.2 4

(ii) (4m2n3 + 16m4 n2 – mn) by 2mn
Samacheer Kalvi 8th Maths Guide Answers Chapter 3 Algebra Ex 3.2 5

Samacheer Kalvi 8th Maths Guide Chapter 3 Algebra Ex 3.2

(iii) 5xy2 – 18x2y3 + 6xy by 6xy
Samacheer Kalvi 8th Maths Guide Answers Chapter 3 Algebra Ex 3.2 6

(iv) 81(p4 q2 r3 + 2p3q3 r2 – 5p2q2r2) by (3pqr)2
Samacheer Kalvi 8th Maths Guide Answers Chapter 3 Algebra Ex 3.2 7
= \(\frac{81}{9}\)(p2q2r2)1-1 (p2r + 2pq – 5)
= 9(p2r + 2pq – 5) = 9 p2r + 18pq – 45

Samacheer Kalvi 8th Maths Guide Chapter 3 Algebra Ex 3.2

Question 6.
Identify the errors and correct them.
(i) 7y2 – y2 + 3y2 = 10y2
Answer:
7y2 – y2 + 3y2 = 10y2 = (7 – 1 + 3)y2
= (6 + 3)y2
= 9y2

(ii) 6xy + 3xy = 9x2y2
Answer:
6xy + 3xy = (6 + 3) xy
= 9 xy

(iii) m(4m – 3) = 4m2 – 3
Answer:
m(4m – 3) = m(4m) + m(-3)
= 4m2 – 3m

Samacheer Kalvi 8th Maths Guide Chapter 3 Algebra Ex 3.2

(iv) (4n)2 – 2n + 3 = 4n2 – 2n + 3
Answer:
(4n)2 – 2n + 3 = 16n2 – 2n + 3

(v) (x – 2)(x + 3) = x2 – 6
Answer:
(x – 2)(x + 3) = x(x + 3) – 2 (x + 3)
= x(x) + (x) × 3 + (-2) (x) + (-2) (3)
= x2 + 3x – 2x – 6
= x2 + x – 6

(vi) -3p2 + 4p – 7 = -(3p2 + 4p – 7)
Answer:
-3p2 + 4p – 7 = -(3p2 – 4p + 7)

Question 7.
Statement A: If 24p2q is divided by 3pq, then the quotient is 8p.
Statement B: Simplification of \(\frac{(5 x+5)}{5}\) is 5x.
(i) Both A and B are true
(ii) A is true but B is false
(iii) A is false but B is true
(iv) Both A and B are false
Answer:
(ii) A is true but B is false
Hint:
Samacheer Kalvi 8th Maths Guide Answers Chapter 3 Algebra Ex 3.2 8

Samacheer Kalvi 8th Maths Guide Chapter 3 Algebra Ex 3.2

Question 8.
Statement A: 4x2 + 3x – 2 = 2(2x2 + \(\frac{3 x}{2}\) – 1)
Statement B: (2m – 5) – (5 – 2m) = (2m – 5) + (2m – 5)
(i) Both A and B are true
(ii) A is true but B is false
(iii) A is false but B is true
(iv) Both A and B are false
Answer:
(i) Both A and B are true
Hint:
(2m – 5) – (5 – 2m) = 2m – 5 – 5 + 2m = 4m – 10
(2m – 5) + (2m – 5) = 4m – 10

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