1. 5(x+7)+(x-6)(x+6) 2. (3a-2)(3a+2)-(1+a)(a-1) 3. (x+3)2 - (x -4)2 4. (2y + 3) (2y - 3) - 3y2 5. (a - 3) (3 + a) + (a - 3)2 6. (x + 3) (x - 3) - 82 + 2x 7. (a - 3)2 - а(а - 3) при а = 1,7 8. 2(3x + 1)? при х = - 3

Let’s solve each of the expressions step by step: 1. **\(5(x+7)+(x-6)(x+6)\)** - First, simplify the expression: \[ 5(x + 7) = 5x + 35 \] \[ (x - 6)(x + 6) = x^2 - 36 \quad \text{(Difference of squares)} \] - Combine everything: \[ 5x + 35 + x^2 - 36 = x^2 + 5x - 1 \] - **Final answer: \(x^2 + 5x - 1\)** 2. **\((3a-2)(3a+2)-(1+a)(a-1)\)** - Use the difference of squares: \[ (3a-2)(3a+2) = 9a^2 - 4 \] \[ (1+a)(a-1) = a^2 - 1 \] - Combine: \[ 9a^2 - 4 - (a^2 - 1) = 9a^2 - 4 - a^2 + 1 = 8a^2 - 3 \] - **Final answer: \(8a^2 - 3\)** 3. **\((x+3)^2 - (x - 4)^2\)** - Use the difference of squares: \[ (x+3 - (x-4))(x+3 + (x-4)) = (7)(2x - 1) \] - **Final answer: \(14x - 7\)** 4. **\((2y + 3)(2y - 3) - 3y^2\)** - Use the difference of squares: \[ (2y + 3)(2y - 3) = 4y^2 - 9 \] - Combine: \[ 4y^2 - 9 - 3y^2 = y^2 - 9 \] - **Final answer: \(y^2 - 9\)** 5. **\((a - 3)(3 + a) + (a - 3)^2\)** - Expand the first part: \[ (a - 3)(3 + a) = a^2 + 3a - 3a - 9 = a^2 - 9 \] - Expand the second part: \[ (a - 3)^2 = a^2 - 6a + 9 \] - Combine: \[ (a^2 - 9) + (a^2 - 6a + 9) = 2a^2 - 6a \] - **Final answer: \(2a^2 - 6a\)** 6. **\((x + 3)(x - 3) - 82 + 2x\)** - Use the difference of squares: \[ (x + 3)(x - 3) = x^2 - 9 \] - Combine: \[ x^2 - 9 - 82 + 2x = x^2 + 2x - 91 \] - **Final answer: \(x^2 + 2x - 91\)** 7. **\((a - 3)^2 - a(a - 3)\) when \(a = 1.7\)** - First, calculate \((a - 3)^2\): \[ (1.7 - 3)^2 = (-1.3)^2 = 1.69 \] - Then calculate \(a(a - 3)\): \[ 1.7(1.7 - 3) = 1.7(-1.3) = -2.21 \] - Finally combine: \[ 1.69 - (-2.21) = 1.69 + 2.21 = 3.90 \] - **Final answer: \(3.90\)** 8. **\(2(3x + 1)^2\) when \(x = -3\)** - First, calculate \(3x + 1\): \[ 3(-3) + 1 = -9 + 1 = -8 \] - Now calculate \((3x + 1)^2\): \[ (-8)^2 = 64 \] - Finally multiply: \[ 2 \times 64 = 128 \] - **Final answer: \(128\)** You can use these solutions to study or review the material for your exams! If you have any more questions or need further assistance, feel free to ask!