Simplification

1. (a+b)²  = a² + b² + 2ab

2. (a - b)² = a² + b² – 2ab

3. a² – b² = (a+b) (a-b)

4. (a + b)³ = a³ + b³ + 3ab(a+b)

5. (a - b)³ = a³ – b³ – 3ab(a-b)

6. a³+b³ = (a+b) (a²+b²-ab)

7. a³ – b³ = (a-b) (a²+b²+ab)

Q. 1. Find the value of  (213*213 + 187*187).

Ans:-     (a²+b²) =  ½ {(a+b)² + (a-b)²}

                           = ½  {(213+187)² + (213-187)

                           = ½ {(400)² + (26)²}

                           = ½ (160000 + 676) = 160676/2 = 80338

Q. 2. Find the value of (983*983)-(617*617).

Ans:-     Acc. To (a² – b²) = (a+b) (a-b)

                            (983)² – (617)² = (983+617) (983-617)

                                                       =  1600*366  =  585600

Q. 3. Find the value of  (743*743*743 + 257*257*257) / (743*743 – 743*257 + 257*257) .

Ans:-    let  a = 743  and   b = 257

         { (743)³ +(257)³} / {(743)² – 743*257 + (257)²} = (a³ + b³) / (a²-ab+b²) 

                              we know (a³ + b³) = (a+b)(a²+b²-ab)

                   (a³ + b³) / (a²-ab+b²) =   {(a+b) (a²+b²-ab)} / (a²+b²-ab)}   =   (a+b)

          =   (743 + 257)

          =   1000

         Solve this question:-

Q. 1. Find the value of 

(689*689*689 – 278*278*278) / (689*689 + 689*278 + 278*278).
Computer Terms Full Name Part 1
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