Samacheer Kalvi 8th Maths Guide Chapter 3 Algebra Ex 3.1

Tamilnadu State Board New Syllabus Samacheer Kalvi 8th Maths Guide Pdf Chapter 3 Algebra Ex 3.1 Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 3 Algebra Ex 3.1

Question 1.
Complete the table.

Answer:

Question 2.
Find the product of the terms.
(i) -2mn, (2m)², -3mn
(ii) 3x²y , -3xy³, x²y²
Answer:
(i) (-2mn) × (2m)² × (-3mn) = (-2mn) × 2²m² × (-3mn) = (- 2mn) × 4m² × (- 3mn)
= (-) (+)(-) (2 × 4 × 3) (m × m² × m) (n × n)
= +24 m⁴ 4n²

(ii) (3x²y) × (-3xy³) × (x²y²) = (+) × (-) × (+) × (3 × 3 × 1)(x² × x × x²) × (y × y³ × y²)
= -9x⁵ y⁶

Question 3.
If l = 4pq², b = -3p²q h = 2p³q³ then, find the value of l × b × h.
Answer:
Given l = 4pq²
b = -3p²q
h = 2p³q³
l × b × h = (4pq²) × -3p²q × 2p³q³
= (+) (-) (+) (4 × 3 × 2) (p × p² × p³) (q × q² × q³)
= – 24p⁶q⁶

Question 4.
Expand
(i) 5x(2y – 3)
(ii) -2p(5p² – 3p + 7)
(iii) 3mn(m³n³ – 5m²n + 7mn²)
(iv) x²(x + y + z)+ y²(x+ y + z) + z²(x – y – z)
Answer:
(i) 5x(2y – 3)
5x(2y -.3) = (5x)(2y) – (5x)(3)
= (5 × 2) (x × y) – (5 × 3)x
= 10xy – 15x

(ii) -2p(5p² – 3p + 7)
-2p (5p² -3p + 7) = (-2p) (5p²) + (-2p) (-3p) + (-2p) (7)
= [(-) (+) (2 × 5) (p × p²)] + [(-) (-) (2 × 3) (p × p)] + (-)(+)(2 × 7)p
= -10p³ + 6p² – 14p

(iii) 3mn(m³n³ – 5m²n + 7mn²)
3mn(m³n³ – 5m²n + 7 mn²) = (3mn) (m³n³) + (3mn) (-5m³n) + (3mn)(7mn³)
= (3)(m ×m³) (n × n³) + (+)(-)(3 × 5)(m × m²)(n × n)+ (3 × 7) (m × m)(n × n²)
= 3m⁴n⁴ – 15m³n² + 21m²n³

(iv) x²(x + y + z)+ y²(x+ y + z) + z²(x – y – z)
x²(x + y + z) + y²(x + y + z) + z²(x – y – z) = (x² × x) + (x² × y) + (x² × z) + (y² × x) + (y² × y) + (y² × z) + (z² × x) + z² (-y) + z² (-z)
= x³ + x²y + x²z + xy² + y³ + y²z + xz² – yz² – z³
= x³ + y³ – z³ + x²y + x²z + xy² + zy² + xz² – yz²

Question 5.
Find the product of
(i) (2x + 3)(2x – 4)
(ii) (y² – 4)(2y² + 3y)
(iii) (m² – n)(5m²n² – n²)
(iv) 3(x – 5) × 2(x – 1)
Answer:
(i) (2x + 3)(2x – 4)
(2x + 3)(2x – 4) = (2x)(2x – 4) + 3(2x – 4)
= (2x × 2x) – 4(2x) – 3(2x) – 3(4)
= 4x² – 8x + 6x – 12
= 4x² + (- 8 + 6)x – 12
= 4x² – 2x – 12

(ii) (y² – 4)(2y² + 3y)
(y² – 4)(2y² + 3y) = y²(2y² + 3y) – 4(2y²) – 4(3y)
= y²(2y²) + y² (3y) – 4(2y²) – 4 (3y)
= 2y⁴ + 3y³ – 8y² – 12y

(iii) (m² – n)(5m²n² – n²)
(m² – n)(5m² n² – n²) = m² (5m²n² – n²) – n (5m²n² – n²)
= m² (5m²n²) + m² (-n²) – n (5m²n² ) + (-) (-) n (n²)
= 5m⁴n² – m²n² – 5m²n³ + n³

(iv) 3(x – 5) × 2(x – 1)
3(x – 5) × 2(x – 1) = (3 × 2) (x – 5) (x – 1)
= 6 × [x (x – 1) – 5 (x – 1)]
6 [x.x – x.1 – 5x + (-1)(-)5 1]
= 6[x² – x – 5x + 5] = 6[x² + (-1 – 5)x + 5]
= 6[x² – 6x + 5] = 6x² – 36 x + 30

Question 6.
Find the missing term.
(i) 6xy × ______ = -12x³y
Answer:
6xy × (-2x²) = -12x³y

(ii) ______ × (-15m²n³p) = 45m³n³p²
Answer:
-3mp × (-15m²n³p) = 45m³n³p²

(iii) 2y(5x²y – ____ + 3____ ) = 10x²y² – 2xy + 6y³
Answer:
2y(5x²y – x + 3y²) = 10x²y² – 2xy + 6y³

Question 7.
Match the following

(A) iv, v, ii, i, iii
(B) v, iv, iii, ii, i
(C) iv, v, ii, iii, i
(D) iv, v, iii, ii, i
Answer:
(C) iv, v, ii, iii, i
a) – iv
b) – v
c) – ii
d) – iii
e) – i

Question 8.
A car moves at a uniform speed of (x + 30) km/hr. Find the distance covered by the car in (y + 2)hours. (Hint: distance = speed × time).
Answer:
Speed of the car = (x + 30) km/hr.
Time = (y + 2) hours
Distance = Speed × time
= (x + 30) (y + 2) = x(y + 2) + 30(y + 2)
= (x) (y) + (x) (2) + (30) (y) + (30) (2)
= xy + 2x + 30y + 60
Distance covered = (xy + 2x + 30y + 60) km

Objective Type Questions

Question 9.
The product of 7p³ and (2p²)² is
(A) 14p¹²
(B) 28p⁷
(C) 9p⁷
(D) 11p¹²
Answer:
(B) 28p⁷

Question 10.
The missing terms in the product -3m³n × 9(_) = _______ m⁴n³ are
(A) mn², 27
(B) m²n, 27
(C) m²n², – 27
(D) mn², – 27
Answer:
(A) mn², 27

Question 11.
If the area of a square is 36x⁴y² then, its side is _________ .
(A) 6x⁴y²
(B) 8x²y²
(C) 6x²y
(D) -6x²y
Answer:
(C) 6x²y

Question 12.
If the area of a rectangle is 48m²n³ and whose length is 8mn² then, its breadth is _____ .
(A) 6 mn
(B) 8m²n
(C) 7m²n²
(D) 6m²n²
Answer:
(A) 6 mn

Question 13.
If the area of a rectangular land is (a² – b²) sq.units whose breadth is(a – b) then, its length is_________
(A) a – b
(B) a + b
(C) a² – b
(D) (a + b)²
Answer:
(B) a + b