\(6x\left(x+y\right)+\left(4x-7\right)\left(x-2y\right)\\ =6x^2+6xy+\left(4x^2-7x\right)-\left(8xy-14y\right)\\ =6x^2+6xy+4x^2-7x-8xy+14y\\ =\left(6x^2+4x^2\right)+\left(6xy-8xy\right)-7x+14y\\ =10x^2-2xy-7x+14y\)
\(\left(5x+1\right)\left(3x-y\right)-\left(x-\dfrac{1}{2}y\right)\left(5x+3\right)\\ =\left[\left(15x^2+3x\right)-\left(5xy+y\right)\right]-\left[\left(5x^2-\dfrac{5}{2}xy\right)+\left(3x-\dfrac{3}{2}y\right)\right]\\ =15x^2+3x-5xy-y-\left(5x^2-\dfrac{5}{2}xy+3x-\dfrac{3}{2}y\right)\\ =15x^2+3x-5xy-y-5x^2+\dfrac{5}{2}xy-3x+\dfrac{3}{2}y\\ =\left(15x^2-5x^2\right)+\left(3x-3x\right)+\left(-5xy+\dfrac{5}{2}xy\right)+\left(-x+\dfrac{3}{2}y\right)\\ =10x^2-\dfrac{5}{2}xy+\dfrac{1}{2}y\)
