Tamilnadu State Board New Syllabus Samacheer Kalvi 9th Maths Guide Pdf Chapter 3 இயற்கணிதம் Ex 3.6 Textbook Questions and Answers, Notes.

## TN Board 9th Maths Solutions Chapter 3 இயற்கணிதம் Ex 3.6

கேள்வி 1.
பின்வருவனவற்றைக் காரணிப்படுத்துக.
(i) x2 + 10x + 24
விடை:
x2 + 10x + 24
=x2 + 4x + 6x + 24
= x (x + 4) + 6(x + 4)
= (x + 4) (x + 6)

(ii) z2 + 4z – 12
விடை : z2 + 4z – 12
= z2 + 6z – 2z – 12
= z (z + 6) – 2(z + 6)
= (z + 6) (z – 2)

(iii) p2 – 6p – 16
விடை:
p2 – 6p – 16
= p2 – 8p + 2p – 16
= p (p – 8) + 2(p – 8)
= (p – 8) (p + 2)

(iv) t2 +72 – 17t
விடை : t2 +72 – 17t
= t2 – 8t – 9t + 72

கேள்வி 2.
பின்வருவனவற்றை காரணிப்படுத்துக.
i) 2a2 + 9a + 10
விடை:
2a2 + 9a + 10
= 2a2 + 4a + 5a + 10
= 2a (a + 2) + 5(a +2)
= (a + 2) (2a +5)

(ii) 5x2 – 29xy – 42y2
விடை:
5x2 – 29xy – 42y2
= 5x2 – 35xy + 6xy – 42y2
= 5x (x – 7y) + 6y (x – 7y)
= (5x + 6y) (x – 7y)

(iii) 8x2 – 18x + 9
விடை:
8x2 – 18x + 9
(2x – 3) (4x – 3)

(iv) 6x2 + 16xy + 8y2
விடை:
6x2 + 16xy + 8y2
= 6x2 + 12xy +4xy + 8y2
= 3x (2x + 4y) + 2y (2x + 4y)
= (3x + 2y) (2x + 4y)

(v) 12x2 + 36x2y + 27x2y2
விடை:
12x2 + 36x2y + 27x2y2
= 3x2 (4 + 12y + 9y2)
= 3x2 (9y2 + 12y + 4)
= 3x2 (9y2 + 6y + 6y + 4)
= 3x2 (3y (3y + 2) + 2 (3y + 2)
= 3x2 (3y + 2) (3y + 2)

(vi) (a + b)2 + 9(a + b) + 18
விடை:
(a + b)2 + 9(a + b) = 18
a + b = x என்க.
x2 + 9x + 18
x2 + 6x + 3x + 18
x (x + 6) + 3 (x + 6)
(x + 3) (x + 6)
(a + b + 3) (a + b + 6)

கேள்வி 3.
பின்வருவனவற்றை காரணிப்படுத்துக.
(i) (p – q)2 – 6(p – q) – 16
விடை:
(p – q)2 – 6(p – q) – 16
p – q = y என்க.
= y2 – 6y – 16
= y2 – 8y + 2y – 16
= y (y – 8) + 2(y – 8)
= (y – 8) (y + 2)
= (p – q – 8) (p – q + 2)

(ii) m2 + 2mn – 24n2
விடை:
m2 + 2mn – 24n2
m2 + 6mn – 4mn – 24n2
m (m + 6n) – 4n (m + 6n)
(m – 4n) (m + 6n)

(iii) √5 a2 + 2a – 3√5
விடை:
√5a2 + 2a – 3√5
= √5a2 + 5a – 3a – 3√5
= a√5 (a + √5 )-3(a + √5)
= (a√5 – 3) (a + √5)

(iv) a4 – 3a2 + 2
விடை:
a4 – 3a2 + 2
= a4 – 2a2 – a2 + 2.
= a2 (a2 – 2) -1 (a2 – 2)
= (a2 – 1) (a2 – 2)
= (a – 1) (a + 1) (a2 – 2)

(v) 8m3 – 2m2n – 15mn2
விடை:
8m3 – 2m2n – 15mn2
= m (8m2 – 2mn – 15n2)
= m (8m2 – 12mn + 10mn – 15n2)
= m (4m (2m – 3n) + 5n (2m – 3n)
= m (4m + 5n) (2m – 3n)

(vi) $$\frac{1}{x^{2}}+\frac{1}{y^{2}}+\frac{2}{x y}$$
விடை:
$$\frac{1}{x^{2}}+\frac{1}{y^{2}}+\frac{2}{x y}$$