Solve (22-8k)^2-4(25)(k^2-6k-7)

$$( 22 - 8 k ) ^ { 2 } - 4 ( 25 ) ( k ^ { 2 } - 6 k - 7 )$$

Evaluate

$$1184+248k-36k^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(22-8k\right)^{2}.

$$484-352k+64k^{2}-4\times 25\left(k^{2}-6k-7\right)$$

Multiply 4 and 25 to get 100.

$$484-352k+64k^{2}-100\left(k^{2}-6k-7\right)$$

Use the distributive property to multiply -100 by k^{2}-6k-7.

$$484-352k+64k^{2}-100k^{2}+600k+700$$

Combine 64k^{2} and -100k^{2} to get -36k^{2}.

$$484-352k-36k^{2}+600k+700$$

Combine -352k and 600k to get 248k.

$$484+248k-36k^{2}+700$$

Add 484 and 700 to get 1184.

$$1184+248k-36k^{2}$$

Expand

$$1184+248k-36k^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(22-8k\right)^{2}.

$$484-352k+64k^{2}-4\times 25\left(k^{2}-6k-7\right)$$

Multiply 4 and 25 to get 100.

$$484-352k+64k^{2}-100\left(k^{2}-6k-7\right)$$

Use the distributive property to multiply -100 by k^{2}-6k-7.

$$484-352k+64k^{2}-100k^{2}+600k+700$$

Combine 64k^{2} and -100k^{2} to get -36k^{2}.

$$484-352k-36k^{2}+600k+700$$

Combine -352k and 600k to get 248k.

$$484+248k-36k^{2}+700$$

Add 484 and 700 to get 1184.

$$1184+248k-36k^{2}$$