Samacheer Kalvi 9th Maths Solutions Chapter 3 Algebra Ex 3.6

   

You can Download Samacheer Kalvi 9th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 3 Algebra Ex 3.6

9th Maths Exercise 3.6 Question 1.
Factorise the following:
(i) x2 + 10x + 24
(ii) z2 + 4z – 12
(iii) p2 – 6p – 16
(iv) t2 + 72 – 17t
(v) y2 – 16y – 80
(vi) a2 + 10a – 600
Solution:
(i) x2 + 10x + 24
x2 + 10x + 24 = x2 + 6x + 4x + 24
9th Maths Exercise 3.6 Samacheer Kalvi
= x(x + 6) + 4 (x + 6)
= (x + 6) (x + 4)

(ii) z2 + 4z – 12
z2 + 4z – 12 = z2 + 6z – 2z- 12
Exercise 3.6 Class 9 Samacheer Kalvi
= z (z + 6) – 2 (z + 6)
= (z + 6) (z – 2)

(iii) p2 – 6p – 16
p2 – 6p – 16 = p2 – 8p + 2p – 16
Ex 3.6 Class 9 Samacheer Kalvi
= p(p – 8) + 2(p – 8)
= (p – 8)(p + 2)

(iv) t2 + 72 – 17t
t2 + 72 – 17t = t2 – 17t + 72
= t2 – 9t – 8t + 72
Exercise 3.6 Class 10 Samacheer Kalvi
= t(t – 9) – 8 (t – 9)
= (t – 9) (t – 8)

(v) y2 – 16y – 80
y2 – 16y – 80 = y2 – 20y + 4y – 80
9th Standard Maths Exercise 3.6 Samacheer Kalvi
= y(y – 20) + 4 (y – 20)
= (y – 20) (y + 4)

(vi) a2 + 10a – 600
a2 + 10a – 600 = a2 + 30a – 20a – 600
Samacheer Kalvi 9th Maths Chapter 3
= a(a + 30) -20 (a + 30)
= (a + 30) (a – 20)

Exercise 3.6 Class 9 Question 2.
Factorise the following
(i) 2a2 + 9a + 10
(ii) 5x2 – 29xy – 42y2
(iii) 9 – 18x + 18x2
(iv) 6x2 + 16xy + 8y2
(v) 12x2 + 36x2y + 27y2x2
(vi) (a + b)2 + 9 (a + b) + 18
Solution:
(i) 2a2 + 9a + 10
2a2 + 9a + 10 = 2a2 + 4a + 5a + 10
Tamilnadu Samacheer Kalvi 9th Maths Solutions Samacheer Kalvi
= 2a(a + 2) + 5 (a + 2)
= (a+ 2) (2a+ 5)

(ii) 5x2 – 29xy – 42y2
5x2 – 35xy + 6xy – 42y2
Samacheer Kalvi 9th Maths Chapter 3 Algebra Ex 3.6 8
= 5x (x – 7) + 6y (x – 7)
= (x – 7) (5x + 6y)

(iii) 9 – 18x + 8x2
= 8x2 – 18x + 9
= 8x2 – 6x – 12x + 9
Samacheer Kalvi 9th Maths Chapter 3 Algebra Ex 3.6 9
= 2x (4 x – 3) – 3 (4x – 3)
= (4x – 3) (2x – 3)

(iv) 6x2 + 16xy + 8y2
= 2 (3x2 + 8xy + 4y2)
= 2 (3x2 + 8xy + 4y2)
Samacheer Kalvi 9th Maths Chapter 3 Algebra Ex 3.6 10
= 2 (3x2 + 6xy + 2xy + 4y2)
= 2 (3x (x + 2y) + 2y (x + 2y))
= 2 (x + 2y) (3x + 2y)

(v) 12x2 + 36x2y + 27y2x2
= 27y2x2 + 36x2y + 12x2 = 3x2(9y2 + 12y + 4)
Samacheer Kalvi 9th Maths Chapter 3 Algebra Ex 3.6 11
= 3x2 (9y2 + 6y + 6y + 4) = 3x2 (3y (3y + 2) + 2 (3y + 2))
= 3x2 (3y + 2) (3y + 2) = 3x2 (3y + 2) (3y + 2)

(vi) (a + b)2 + 9 (a + 6) + 18
= (a + b)2 + 6 (a + b) + 3 (a + b) + 18
Samacheer Kalvi 9th Maths Chapter 3 Algebra Ex 3.6 12
= (a + b) ((a + b) + 6) + 3 ((a + b) + 6)
= ((a + 6) + 6) ((a + b) + 3) = (a + b + 6) (a + b + 3)

 

Ex 3.6 Class 9 Question 3.
Factorise the following:
(i) (p – q)2 – 6(p – q) – 16
(ii) m2 + 2mn – 24n2
(iii) \(\sqrt{5} a^{2}\) + 2a – \(3 \sqrt{5}\)
(iv) a4 – 3a2 + 2
(v) 8m3 – 2m2n – 15mn2
(vi) \(\frac{1}{x^{2}}+\frac{1}{y^{2}}+\frac{2}{x y}\)
Solution:
(i) (p – q)2 – 6 (p – q) – 16
= (p – q)2 – 8(p – q) + 2(p – q) – 16
Samacheer Kalvi 9th Maths Chapter 3 Algebra Ex 3.6 13
= (p – q)((p – q) – 8) + 2((p – q) – 8)
= (p – q – 8)(p – q + 2)

(ii) m2 + 2mn – 24n2
= m2 + 6mn – 4mn – 24n2
Samacheer Kalvi 9th Maths Chapter 3 Algebra Ex 3.6 14
= m(m + 6n) – 4n(m + 6n)
= (m + 6n)(m – 4n)

Samacheer Kalvi 9th Maths Chapter 3 Algebra Ex 3.6 15