Question

40.Utilizand formulele de calcul prescurtat , calculati: a) 3(x+2)la puterea 2 - (x-1)la puterea 2+2(x-3)(x+3)=... b) (2x-1supra2)la puterea 2 + (3x+1)la puterea 2 - (2 supra 3 x - 5)(2 supra3 x + 5)=.... c) (4x-y)la puterea 2 + (2x-5y)(2x+5y)-3(3x+y)la puterea 2 = .... d) (radical3x+1)la puterea 2 +2 (radical 5x +1)(radical 5x-1)-(radical 3x - 2) la puterea 2 = ... e) (radical3-2x) la puterea 2 - (radical15+ radical3x)la puterea2 - 2(radical3x - 3 radical 2 )(radical3x+3radical2) = ..... Va roooog muult 

Answer 1

$a)3(x+2)^{2} -(x-1)^{2} +2(x-3)(x+3)= \\ 3(x^{2} +2x+4)-(x^{2} -2x+1)+2(x^{2} +3x-3x-9)= \\3 x^{2} +6x+12- x^{2} +2x-1+2 x^{2} -18= \\ =4 x^{2} +8x-7 \\b) (\frac{2x-1}{2})^{2}+(3x+1)^{2} -( \frac{2}{3x-5})( \frac{2}{3x+5} ) \\ \frac{4 x^{2} -2x+1}{4} +9 x^{2} +6x+1- \frac{4}{ 9x^{2}-25 } \\ \\ c ^)(4x-y) ^{2}+(2x-5y)(2x+5y)-3(3x+y)^{2}= \\ 16 x^{2} -8xy+y^{2}+4 x^{2} -25y^{2} -3(9 x^{2} +6xy+y^{2})= \\ 16 x^{2} -8xy+y^{2}+4 x^{2} -25y^{2} -27 x^{2} -18xy-3y^{2} = \\7 x^{2} -26xy-27 ^{2}$