Prove that if x is odd then x² is also odd | Math Important Question

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Let x be an odd integer. Prove x^2 is odd. Let x be an odd integer. Prove x^2 is odd.
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If P and Q are of (x+a)ⁿ then prove that(i)P² -Q²=(x²-a²)ⁿ (ii) 4PQ=(x+a)²ⁿ -(x-a)²ⁿ If P and Q are of (x+a)ⁿ then prove that(i)P² -Q²=(x²-a²)ⁿ (ii) 4PQ=(x+a)²ⁿ -(x-a)²ⁿ
Prove that if x and y are odd positive integers, then x²+y² is even , but not divisible by 4. Prove that if x and y are odd positive integers, then x²+y² is even , but not divisible by 4.
If x and y are two odd positive integers, show that x2 + y2 is even but not divisible by 4. If x and y are two odd positive integers, show that x2 + y2 is even but not divisible by 4.