Solve 9left(n-2yright)^2-4left(n-2yright)-13

$$9 { \left(n-2y \right) }^{ 2 } -4 \left( n-2y \right) -13$$

Evaluate

$$\left(-18y+9n-13\right)\left(1+n-2y\right)$$

Solution Steps

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

$$9\left(n^{2}-4ny+4y^{2}\right)-4\left(n-2y\right)-13$$

Use the distributive property to multiply 9 by n^{2}-4ny+4y^{2}.

$$9n^{2}-36ny+36y^{2}-4\left(n-2y\right)-13$$

Use the distributive property to multiply -4 by n-2y.

$$9n^{2}-36ny+36y^{2}-4n+8y-13$$

Expand

$$36y^{2}-36ny+8y+9n^{2}-4n-13$$

Solution Steps

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

$$9\left(n^{2}-4ny+4y^{2}\right)-4\left(n-2y\right)-13$$

Use the distributive property to multiply 9 by n^{2}-4ny+4y^{2}.

$$9n^{2}-36ny+36y^{2}-4\left(n-2y\right)-13$$

Use the distributive property to multiply -4 by n-2y.

$$9n^{2}-36ny+36y^{2}-4n+8y-13$$