(x + 1)((x + 2) + (x - 2)) = (x + 1)(2x) = 2x² + 2x.

(x + 1)(x - 1) = x² - 1, which is the difference of squares.

(x + 2)(x - 2) = x² - 4 by the difference of squares identity.

(x + 2)² = x² + 4x + 4; thus, (x + 2)² - (x² + 4) = 4x.

(x + 3)(x - 3) = x² - 9 by the difference of squares formula.

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx by the expansion of the square of a trinomial.

(x + y)(x - y) = x² - y² by the difference of squares identity.

(x - 4)(x + 4) = x² - 16.

Multiplying three negative ones gives −1.

(−1)^3 = −1.

(−1)² = 1 and (−2)² = 4, so 1 + 4 = 5.

(−1)³ = −1.

(−2)² = 4.

(−5)² = 25.

−7 + (−3) = −10.

(√(49) + √(16)) = 7 + 4 = 11, so 11 / 5 = 2.2, which rounds to 2.

According to BODMAS, 4 × 2 = 8, so 3 + 8 = 11.

3.5 + 2.8 = 6.3.

3² = 9 and 4² = 16. So, 9 + 16 = 25.

3√(27) = 3 × 3 = 9.

7^2 = 7 × 7 = 49.

Cotangent is the reciprocal of tangent. Since tan 60° = √3, cot 60° = 1/√3.

Cosecant is the reciprocal of sine. Since sin 30° = 1/2, csc 30° = 1 / (1/2) = 2.

The discriminant must be non-negative: (2k)^2 - 4(1)(16) ≥ 0. This gives 4k^2 - 64 ≥ 0, leading to k^2 ≥ 16, so k ≥ 4.

The discriminant must be less than zero. Thus, k^2 - 4*1*16 < 0 leads to k^2 < 64, giving k < 8 and k > -8.

For the roots to be equal, the discriminant must be zero. Thus, k^2 - 4*1*16 = 0, which gives k^2 = 64, so k = ±8.

For equal roots, the discriminant must be zero. Thus, k^2 - 4*1*4 = 0, which gives k^2 = 16, so k = ±4.

For both roots to be negative, k must be negative and greater than the square root of the discriminant. Thus, k < -6.

The sum of the roots is 3 + 3 = 6, so k = 6.

The sum of the roots is 3 + 3 = 6, so k = 6.