Prove (n + 6)² – (n + 2)² is always a multiple of 8. (Use direct proof.)

CAN YOU PLEASE SHOW WORK AND CAN YOU PLEASE DO THIS FASTT THANK YOU

Find the term of (a – 2b)3 that has b in it. |

Q3. Expand and simplify(i) (2k − 3)(k − 2)

If n = 12 m (me N), prove that n "C2 "Co- - n "C4 "C6 (2+√3)² (2+√3)² (2+√3)6 +···=(−1)” 2√2 1+√3 n

For each positive integer n, define an = 1/2 (C₂ (2 + √3)² + (2 − √3)”). - It is known that an is a positive integer for each n. Find the remainder when a2023 is divided by 4. (A) 0 (B) 1 (C) 2 (D) 3

Show that n4 #0 (4n²) by giving a simple argument

(n3+n2logn234n)(2n+n12345)+(567logn10345n+19n)(n3+230)

true of false:   (v) Given an integer n ≥ 2, [a]n ×n [0]n = [a]n for any integer a.

Pls kindly help to prove: when n is even, then (n, (n/2)^2-1, (n/2)^2+1) will be a Pythagorean triple. (need explain (n/2)^2-1 is also a integer).