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.)