[tex]14x(3x - 2y) - {( - 7x + 2y)}^{2} = 14x(3x - 2y) - {( 2y- 7x)}^{2} = 42 {x}^{2} - 28xy - (4 {y}^{2} - 28xy + 49 {x}^{2} ) = 42 {x}^{2} - 28xy - 4 {y}^{2} + 28xy - 49 {x}^{2} = - 7 {x}^{2} - 4 {y}^{2} [/tex]

[tex] - 7 \times {( - \frac{1}{7} )}^{2} - 4 \times {( \frac{1}{2}) }^{2} = - 7 \times \frac{1}{49} - 4 \times \frac{1}{4} = - \frac{1}{7} - 1 = - \frac{8}{7} [/tex]

[tex] {(a - 6b)}^{2} + (a - 6b)(a + 6b) = {a}^{2} - 12ab + 36 {b}^{2} + {a }^{2} - 36 {b}^{2} = 2 {a}^{2} - 12ab[/tex]

[tex]2 \times {( -2)}^{2} - 12 \times ( - 2) \times ( - 6) = 2 \times 4 + 24 \times ( - 6) = 8 - 144 = - 136[/tex]