#### Topics

31.Factorise.

i) 169m2 - 625n2                   ii) 4p2 - 25q2

Ans:

i) 169m2 - 625n2 = (13m)2 - (25n)2

= (13m + 25n)(13m - 25n)

ii) 4p2 - 25q2       = (2p)2 - (5q)2                       [a2 - b2 = (a + b)(a - b)]

= (2p + 5q) (2p - 5q)

32.Factorise

i) x2 +7x + 12               ii) p2 - 6p + 8

Ans:

i) x2 +7x + 12         = x2 + 3x + 4x +12

= x( x+ 3) + 4(x + 3)

= (x + 3) (x + 4)

ii) p2 - 6p + 8         = p2 - 4p - 2p + 8

= p(p - 4) -2(p - 4)

= (p - 4) (p -2)

33.Simplify

(i) 16x4 ÷ 32x                   (ii) -4 2y3 ÷ 7y2

Ans:

34.Simplify

i) (5y3 - 4y2 + 3y) ÷ y               ii) (9x5 - 15x4 - 21x2) ÷ 3x2

Ans:

35.Simplify

i) (x2 + 7x + 10) ÷ (x + 2)               ii) (a2 + 24a + 144) ÷ (a + 12)

Ans:

36.Solve 3x + 5 = 23.

Ans:

3x + 5 = 23 → 3x = 32 - 5 (transposing 5 to R.H.S)

= 18

x = 18/3 = 6.

37.Solve 17 = 10 - y.

Ans:

17 = 10 - y → 17 - 10 = -y (transposing 10 to L H S)

→  7 = -y  → y = 7.

38.Solve 3(3x - 7) = 5(2x - 3).

Ans:

3(3x - 7) = 5(2x - 3) → 9x - 21 = 10x - 15

→ 9x - 10x = -15 + 21

→ -x = 6 → x = 6.

39.

Ans:

40.

Ans:

L CM of 3, 4 and 2 is 12

multiplying throughout by 12,

→ 4m + 3m = 6  → 7m = 6  →

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