a) \(\left(x+2\right)^2+\left(2x-1\right)^2\)
\(=\left(x^2+4x+4\right)+\left(4x^2-4x+1\right)\)
\(=x^2+4x+4+4x^2-4x+1\)
\(=5x^2+5\)
b) \(\left(3x+2\right)^2-\left(x+3\right)^3\)
\(=\left(9x^2+12x+4\right)-\left(x^3+9x^2+27x+27\right)\)
\(=9x^2+12x+4-x^2-9x^2-27x-27\)
\(=-15x-23\)
c) \(\left(3x-2\right)\left(9x^2+6x+4\right)-\left(27x+3\right)\left(x^2+4\right)\)
\(=\left(27x^3-8\right)-\left(27x^3+108x+3x^2+12\right)\)
\(=27x^3-8-27x^3-108x-3x^2-12\)
\(=-3x^2-108x-20\)
d) \(\left(x+2\right)^3-\left(x+4\right)\left(x^2-4x+16\right)\)
\(=\left(x^3+6x^2+12x+8\right)-\left(x^3+64\right)\)
\(=x^3+6x^2+12x+8-x^3-64\)
\(=6x^2+12x-56\)
a) (x + 2)² + (2x - 1)²
= x² + 4x + 4 + 4x² - 4x + 1
= (x² + 4x²) + (4x - 4x) + (4 + 1)
= 5x² + 5
b) (3x + 2)² - (x + 3)³
= 9x² + 12x + 4 - x³ - 9x² - 27x - 27
= -x³ + (9x² - 9x²) + (12x - 27x) + (4 - 27)
= -x³ - 15x - 23
c) (3x - 2)(9x² + 6x + 4) - (27x + 3)(x² + 4)
= (3x)³ - 2³ - 27x³ - 108x - 3x² - 12
= 27x³ - 8 - 27x³ - 108x - 3x² - 12
= (27x³ - 27x³) - 3x² - 108x + (-8 - 12)
= -3x² - 108x - 20
d) (x + 2)³ - (x + 4)(x² - 4x + 16)
= x³ + 3.x².2 + 3.x.2² + 2³ - x³ - 4³
= x³ + 6x² + 12x + 8 - x³ - 64
= (x³ - x³) + 6x² + 12x + (8 - 64)
= 6x² + 12x - 56
