# CLASS-6PROBLEM & SOLUTION ON SUBTRACTION

PROBLEM & SOLUTION ON SUBTRACTION -

Example.1) What should be subtracted from a³- 4a² + 5a – 6 to obtaina a² - 2a + 1?

Ans.)

Let 'X' denote the required

expression, (a³ - 4a² + 5a – 6) – X =  a² - 2a + 1

Hence, X =  (a³ - 4a² + 5a – 6) – (a² - 2a + 1)

= a³ - 4a² + 5a – 6 - a2 + 2a – 1

= a³ - 4a² + 5a – 6 - a² + 2a – 1

= a³ - 5a² + 7a – 7                    (Ans.)

Example.2) Subtract (a³ - 4a² + 5a – 6) from the sum of (3a³ + a² + 1) and (a² - 2)  ?

Ans.)

= [(3a³ + a² + 1) + a² - 2)] - (a³ - 4a² + 5a – 6)

= (3a³ + a² + 1 + a² - 2) - (a³ - 4a² + 5a – 6)

= (3a³ + 2a² - 1) - (a³ - 4a² + 5a – 6)

= 3a³ + 2a² - 1 - a³ + 4a² - 5a + 6

= 3a³ + 2a²- 1 - a³ + 4a² - 5a + 6

= 2a³ + 6a² - 5a + 5                (Ans.)

Example.3) (a)What should be added to x² + xy + y² to obtain 2x² + 3xy ?

(b)What should be subtracted from 2a + 8b + 10 to get -3a + 7b +16 ?

Ans.)

(a)Let 'p' should be added. Then, according to question,

=> x² + xy + y² + p = 2x²+ 3xy

=> p = 2x² + 3xy – (x² + xy + y²)

=> p = 2x² + 3xy x² - xy - y²

=> p = x²+ 2xy - y²

Hence, x² + 2xy - y² should be added. .................(a)          (Ans.)

(b) Let 'q' should be subtracted.

Then, according to question, 2a + 8b +10 – q = -3a + 7b + 16

=> -q = -3a + 7b +16 – (2a + 8b + 10)

=> -q = -3a + 7b + 16 – 2a - 8b – 10

=> -q = -5a – b + 6

=> q = - (-5a – b + 6)         [Multiply (-) sign on both side]

=> q = 5a + b – 6

Hence, 5a + b – 6 should be subtracted. ..................(b)          (Ans.)