Thursday, July 5, 2012

Expansions

1. ( a + b ) 2 = a 2 + 2ab + b 2 2. ( a − b ) 2 = a 2 − 2ab + b 2 3. ( a + b ) ( a − b ) = a 2 − b 2 4. ( a + 1 a ) 2 = a 2 + 1 a 2 + 2 5. ( a − 1 a ) 2 = a 2 + 1 a 2 − 2 6. ( a + 1 a ) ( a − 1 a ) = a 2 − 1 a 2 7. ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) 8. ( a + b ) 3 = a 3 + b 3 + 3ab ( a + b ) = a 3 + 3a 2 b + 3ab 2 + b 3 9. ( a − b ) 3 = a 3 − b 3 − 3ab ( a − b ) = a 3 − 3a 2 b + 3ab 2 − b 3 10. ( a + b ) ( a 2 − ab + b 2 ) = a 3 + b 3 11. ( a − b ) ( a 2 + ab + b 2 ) = a 3 − b 3 12. ( a + b + c ) ( a 2 + b 2 + c 2 − ab − bc − ca ) = a 3 + b 3 + c 3 − 3abc 13. ( x + a ) ( x + b ) ( x + c ) = x 3 + ( a + b + c ) x 2 + ( ab + bc + ca ) x + abc 1. (a+b)^2 = a^2 + 2ab + b^2 newline 2. (a-b)^2 = a^2 - 2ab + b^2 newline 3. (a+b)(a-b)= a^2 -b^2 newline 4. (a +1 over a)^2 = a^2 +1 over a^2 + 2 newline 5. (a - 1 over a)^2 = {a^2} + {1 over {a^2}} - 2 newline 6.(a+1 over a)(a - 1 over a)= a^2 -1 over a^2 newline 7. (a + b +c )^2 = a^2 + b^2 +c^2 + 2(ab + bc +ca) newline 8. (a+b)^3 = a^3 + b^3 + 3ab(a+b) = a^3 + {3a^2}b + 3ab^2 + b^3 newline 9. (a- b)^3 = a^3 - b^3 - 3ab(a-b) = a^3 - {3a^2}b + 3ab^2 - b^3 newline 10. (a+b)(a^2 -ab + b^2) = a^3 + b^3 newline 11. (a-b)(a^2 + ab + b^2) =a^3 - b^3 newline 12. (a+b+c)(a^2 + b^2 + c^2 -ab -bc -ca) = a^3 + b^3 +c^3 -3abc newline 13. (x+a)(x+b)(x+c) = x^3 + (a+b+c)x^2 + (ab +bc +ca)x + abc

See the Video below for problem solving on Expansions



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