Răspuns:
[tex]a) {(4 + 3x)}^{2} - ( {1 + 2x)}^{2} = \\ = ( {4}^{2} + 2 \times 4 \times 3x + ( {3x)}^{2} ) - ( {1}^{2} + 2 \times 1 \times 2x + ( {2x)}^{2} ) = \\ = (16 + 24x + 9 {x}^{2} ) - (1 + 4x + 4 {x}^{2} ) = \\ = 16 + 24x + 9 {x}^{2} - 1 - 4x - 4 {x}^{2} = \\ = 5 {x}^{2} + 20x + 15[/tex]
[tex]b)( {x \sqrt{3} + 2)}^{2} + ( {2x - 5 \sqrt{3}) }^{2} = \\ = (( {x \sqrt{3}) }^{2} + 2 \times x \sqrt{3} \times 2 + {2}^{2} ) + (( {2x)}^{2} - 2 \times 2x \times 5 \sqrt{3} + ( {5 \sqrt{3}) }^{2} ) = \\ = ( {x}^{2} \times 3 + 4x \sqrt{3} + 4) + (4 {x}^{2} - 20x \sqrt{3} + 25 \times 3) \\ = 3 {x}^{2} + 4x \sqrt{3} + 4 + 4 {x}^{2} - 20x \sqrt{3} + 75 = \\ = 7 {x}^{2} - 16x \sqrt{3} + 79[/tex]
