Exercise 10.2

1. If m = 2, find the value of following questions.

(i) m - 2

= - 2 =

(ii) 3m - 5

= 3 × - 5

= - 5 =

(iii) 9 - 5m

= 9 - 5 ×

= 9 - =

(iv) 3m2 - 2m - 7

= 3 (2) - (2 × ) - 7

= - - 7 =

(v) 5m2 4

= [5×2] - 4

= (2) - 4 =

2. If p = – 2, find the value of following questions.

(i) 4p + 7

= 4 × + 7

= + 7 =

(ii) -3p2 + 4p + 7

= -3(-2) + 4() + 7

= -3 × - 8 + 7 =

(iii)-2p2 -3p2 + 4p + 7

-2(-3) -3(-2) + 4 + 7

= (-2×) -(3×) - (+7)

= - - + 7 =

3. Find the value of the following expressions, when x = –1.

Instruction

4. If a = 2, b = – 2, find the value of following questions.

(i)a2 + b2

= 2 + -2

= + =

(ii)a2 + ab + b2

= 2 + 2 × () + -2

= - + =

(iii)a2 - b2

= 2 - (-2)

= - =

5. When a = 0, b = – 1, find the value of the given expressions.

(i)2a + 2b

= (2 × ) + 2 × ()

= 0 + () =

(ii)2a2 + b2 + 1

= 2 × 0 + -2 + 1

= 0 + + =

(iii)2a2b + 2ab2 + ab

= 2 × × × () + 2 × × -2 + × ()

= + + =

(iv)a2 + ab + 2

= 2 + × () + 2

= + + =

6. Simplify the expressions and find the value if x is equal to 2.

(i) x + 7 + 4 (x-5)

Instruction

(ii)3(x + 2) + 5x - 7

(iii)6x + 5 (x - 2)

(iv)4(2x - 1) + 3x + 11

7. Simplify these expressions and find their values if x = 3, a = – 1, b = – 2.

(i)3x - 5 - x + 9 = x + 4

Now putting the value of x = 3 in 2x + 4

= (2 × ) + 3 =

(ii)2 - 8x + 4x + 4 = -x + 6

Now putting the value of x = 3 in -4x + 6

= (-4 × ) + 6 =

(iii)3a + 5 - 8a + 1 = -a + 6

Now putting the value of a = -1 in -5a + 6

= -5 × () + 6 =

(iv)10 - 3b - 4 - 5b = -b + 6

Now putting the value of b = -2 in -8b + 6

= -8 × () + 6 =

(v)2a - 2b - 4 - 5 + a = a - b - 9

Now putting the value of a = -1 and b = -2 in 3a - 2b - 9

= 3 × () × () - 9 =

8. (i) If z = 10, find the value of z3 – 3(z – 10).

The expression z3 - 3(z - 10) = z3 - z + 30

Now putting the value of z = 10

= 103 - (3 × 10) + 30

= - 30 + 30

=

(ii)If p = – 10, find the value of p2 – 2p – 100

= The expression p2 - 2p - 100

Now putting the value of p = -10

= (2) - 2 × () - 100

= + - =

9. What should be the value of a if the value of 2x2 + x – a equals to 5, when x = 0?

Given x =

Also, 2x2 + x - a = 5

Substitute the value of x in given expression

= 2 × 2 + - a = 5

= - a = 5

= -a = 5 ⇒ a =

10. Simplify the expression and find its value when a = 5 and b = – 3.

2(a2 + ab) + 3 - ab

Given, a = and b =

2(a2 + ab) + 3 - ab = 2a2 + ab + 3

Now substitute the given values of a and b in 2a2 + ab + 3.

= 2 × × + × () + 3 =