Question

Simplify

(2x + 5y)(3x + 4y) − (7x + 3y)(2x − y)

Answer 1

(2x +5y)(3x+4y)

$$\begin{gathered} =2\mathrm{x}\times (3\mathrm{x}+4\mathrm{y})+5\mathrm{y}\times (3\mathrm{x}+4\mathrm{y}) \\ =6{\mathrm{x}}^{(1+1)}+8\mathrm{xy}+15\mathrm{yx}+20{\mathrm{y}}^{(1+1)} \\ =6{\mathrm{x}}^2+23\mathrm{xy}+20{\mathrm{y}}^2 \\ (7\mathrm{x}+3\mathrm{y})(2\mathrm{x}+\mathrm{y}) \\ =7\mathrm{x}(2\mathrm{x}+\mathrm{y})+3\mathrm{y}(2\mathrm{x}+\mathrm{y}) \\ =14{\mathrm{x}}^{(1+1)}+7\mathrm{xy}+6\mathrm{yx}+3{\mathrm{y}}^{(1+1)} \\ =14{\mathrm{x}}^2+13\mathrm{xy}+3{\mathrm{y}}^2 \end{gathered}$$

∴ (2x + 5y)(3x + 4y) − (7x + 3y)(2x − y)

$$\begin{gathered} =6{\mathrm{x}}^2+23\mathrm{xy}+20{\mathrm{y}}^2-(14{\mathrm{x}}^2+13\mathrm{xy}+3{\mathrm{y}}^2) \\ =6{\mathrm{x}}^2-14{\mathrm{x}}^2+23\mathrm{xy}-13\mathrm{xy}+20{\mathrm{y}}^2-3{\mathrm{y}}^2 \\ =-8{\mathrm{x}}^2+10\mathrm{xy}+17{\mathrm{y}}^2 \end{gathered}$$