Solve 15left(x-2yright)^2-8left(x-2yright)-16

$$15 { \left(x-2y \right) }^{ 2 } -8 \left( x-2y \right) -16$$

Evaluate

$$\left(3x-6y-4\right)\left(5x-10y+4\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2y\right)^{2}.

$$15\left(x^{2}-4xy+4y^{2}\right)-8\left(x-2y\right)-16$$

Use the distributive property to multiply 15 by x^{2}-4xy+4y^{2}.

$$15x^{2}-60xy+60y^{2}-8\left(x-2y\right)-16$$

Use the distributive property to multiply -8 by x-2y.

$$15x^{2}-60xy+60y^{2}-8x+16y-16$$

Expand

$$15x^{2}-60xy-8x+60y^{2}+16y-16$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2y\right)^{2}.

$$15\left(x^{2}-4xy+4y^{2}\right)-8\left(x-2y\right)-16$$

Use the distributive property to multiply 15 by x^{2}-4xy+4y^{2}.

$$15x^{2}-60xy+60y^{2}-8\left(x-2y\right)-16$$

Use the distributive property to multiply -8 by x-2y.

$$15x^{2}-60xy+60y^{2}-8x+16y-16$$