Solve (n-2y)^2+7(n-2y)+12

$$( n - 2 y ) ^ { 2 } + 7 ( n - 2 y ) + 12$$

Evaluate

$$\left(3+n-2y\right)\left(4+n-2y\right)$$

Solution Steps

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

$$n^{2}-4ny+4y^{2}+7\left(n-2y\right)+12$$

Use the distributive property to multiply 7 by n-2y.

$$n^{2}-4ny+4y^{2}+7n-14y+12$$

Expand

$$4y^{2}-4ny-14y+n^{2}+7n+12$$

Solution Steps

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

$$n^{2}-4ny+4y^{2}+7\left(n-2y\right)+12$$

Use the distributive property to multiply 7 by n-2y.

$$n^{2}-4ny+4y^{2}+7n-14y+12$$