[tex] {(12 - 5x)}^{2} - {(4x + 3)}^{2} = {12}^{2} - 2 \times 12 \times 5x + {(5x)}^{2} - ( ({4x})^{2} + 2 \times 4x \times 3 + {3}^{2}) = 144 - 120x + {25x}^{2} - ( {16x}^{2} + 24x + 9) \: = 144 - 120x + {25x}^{2} - {16x}^{2} - 24x - 9 = {41x}^{2} - 144x + 135[/tex]
[tex] {(3x - 4)}^{2} - {(7x + 2)}^{2} = {(3x)}^{2} - 2 \times 3x \times 4 + {4}^{2} - ( {(7x)}^{2} + 2 \times 7x \times 2 + {2}^{2}) = {9x}^{2} - 24x + 16 - ( {49x}^{2} + 28x + 4) = {9x}^{2} - 24x + 16 - {49x}^{2} - 28x - 4 = -58 {x}^{2} - 4x + 12 = - 2( {29x}^{2} + 2x - 6)[/tex]
