Solve 7(h+k)^2-21(h+k)

$$7 ( h + k ) ^ { 2 } - 21 ( h + k )$$

Evaluate

$$7\left(h+k\right)\left(h+k-3\right)$$

Solution Steps

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

$$7\left(h^{2}+2hk+k^{2}\right)-21\left(h+k\right)$$

Use the distributive property to multiply 7 by h^{2}+2hk+k^{2}.

$$7h^{2}+14hk+7k^{2}-21\left(h+k\right)$$

Use the distributive property to multiply -21 by h+k.

$$7h^{2}+14hk+7k^{2}-21h-21k$$

Expand

$$7h^{2}+14hk-21h+7k^{2}-21k$$

Solution Steps

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

$$7\left(h^{2}+2hk+k^{2}\right)-21\left(h+k\right)$$

Use the distributive property to multiply 7 by h^{2}+2hk+k^{2}.

$$7h^{2}+14hk+7k^{2}-21\left(h+k\right)$$

Use the distributive property to multiply -21 by h+k.

$$7h^{2}+14hk+7k^{2}-21h-21k$$