Question

1.Calculaţi,utilizând formulele de calcul prescurtat:
a)(1+x)²+(2+x)²+(3+x)²
b)(2x+3y)²+(2x+3y)(2x-3y)
c)(2x+3y)²+4x(3x-2)+(2x-1)² Rapid dau coroana

Answer 1

a) 1+2x+x²+4+4x+x²+9+6x+x²= 3x²+12x+14
b) 4x²+12xy+9y²+4x²-9y²=8x²+12xy
c) 4x²+12xy+9y²+12x²-8x+4x²-4x+1=20x²+12xy-12x+9y²+1

Answer 2

$a) \\ \\ (1 + x) ^{2} + (2 + x) ^{2} + (3 + x) ^{2} = \\ \\ 14 + 2x + {x}^{2} + 4x + {x}^{2} + 6x + {x}^{2} = \\ \\ 14 + {3x}^{2} + 12 \\ \\ b) \\ \\ (2x + 3y) ^{2} + (2x + 3y)(2x - 3y) = \\ \\ {4x}^{2} + 12xy + {9y}^{2} + ( {4x}^{2} - {9y}^{2}) = \\ \\ 12xy + {8x}^{2} \\ \\ c) \\ \\ (2x + 3y) ^{2} + 4x(3x - 2) + (2x - 1) = \\ \\ {4x}^{2} + 12xy + {9y}^{2} + ( {12x}^{2} - 8x) + ( {4x}^{2} - 4x + 1) = \\ \\ {20x}^{2} + 12xy + {9y}^{2} - 12x + 1$