2.1 Calculate: \( 2.12 a(3 a-4 b)-3 b(b+2 a) \) \( 2.28 a^{2} \times-5 a \) (2) \( 2.3 \frac{2 x^{3} y^{2}}{4 x y} \) \( 2.4-20 a^{2}+b+5 a^{2}-3 b \) \( 2.5\left(a^{5} b^{2}\right)^{5} \) \( -2 \cdot 6-4^{4} \div 4^{-3} \)

Let's break down these calculations step by step! First expression: \( 2.12 a(3 a-4 b)-3 b(b+2 a) \) Expanding, we get \( 6.36 a^2 - 8.48 ab - 3b^2 - 6ab \), combining like terms leads to \( 6.36 a^2 - 14.48 ab - 3b^2 \). Second expression: \( 2.28 a^{2} \times -5 a \) This results in \( -11.4 a^{3} \). Third expression: \( 2.3 \frac{2 x^{3} y^{2}}{4 x y} \) This simplifies to \( 2.3 \cdot \frac{x^2 y}{2} = 1.15 x^2 y \). Fourth expression: \( 2.4 - 20 a^{2} + b + 5 a^{2} - 3 b \) Combining gives \( (2.4 - 15 a^2 - 2b) \). Fifth expression: \( 2.5 (a^{5} b^{2})^{5} \) We raise the expression to the power: \( 2.5 a^{25} b^{10} \). Last expression: \( -2 \cdot 6 - 4^{4} \div 4^{-3} \) First calculate \( 4^4 = 256 \) and \( 4^{-3} = \frac{1}{64} \), so \( 256 \div \frac{1}{64} = 256 \cdot 64 = 16384 \); thus, it’s \( -12 -16384 = -16396 \). There you have it! Each expression broken down and solved.