Solve (n-k)^2-4n(2k-3n)

$$( n - k ) ^ { 2 } - 4 n ( 2 k - 3 n )$$

Evaluate

$$13n^{2}-10kn+k^{2}$$

Solution Steps

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

$$n^{2}-2nk+k^{2}-4n\left(2k-3n\right)$$

Use the distributive property to multiply -4n by 2k-3n.

$$n^{2}-2nk+k^{2}-8nk+12n^{2}$$

Combine -2nk and -8nk to get -10nk.

$$n^{2}-10nk+k^{2}+12n^{2}$$

Combine n^{2} and 12n^{2} to get 13n^{2}.

$$13n^{2}-10nk+k^{2}$$

Expand

$$13n^{2}-10kn+k^{2}$$

Solution Steps

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

$$n^{2}-2nk+k^{2}-4n\left(2k-3n\right)$$

Use the distributive property to multiply -4n by 2k-3n.

$$n^{2}-2nk+k^{2}-8nk+12n^{2}$$

Combine -2nk and -8nk to get -10nk.

$$n^{2}-10nk+k^{2}+12n^{2}$$

Combine n^{2} and 12n^{2} to get 13n^{2}.

$$13n^{2}-10nk+k^{2}$$