Prove directly:
Given that a, b, c is a Pythagorean triple, prove that qa, qb, and qc is a Pythagorean triple where q is contained in R, q does not equal 0.

Question

Prove directly:
Given that a, b, c is a Pythagorean triple, prove that qa, qb, and qc is a Pythagorean triple where q is contained in R, q does not equal 0.

anonymous · Answer

$$
(qb)^2 + (qc)^2 = q^2 b^2 + q^2 c^2= q^2(b^2+c^2)
$$
Can you finish it now?

anonymous · Answer

Notice that
$$
b^2 + c^2 = a^2
$$

anonymous · Answer

$$
(qb)^2 + (qc)^2 = q^2 b^2 + q^2 c^2= q^2(b^2+c^2)= q^2 a^2

$$

anonymous · Answer

$$
q^2 a^2 = (qa)^2
$$

anonymous · Answer

Can you explain in more detail from the first step.

anonymous · Answer

Do you know that
$$

(x y)^2= x^2 y^2 $$?

anonymous · Answer

Do you know that $ mn + m p = m(n+p)   $?

anonymous · Answer

yes I do

anonymous · Answer

In this case, you should understand step 1

anonymous · Answer

yes

anonymous · Answer

Do you understand the whole process now?

anonymous · Answer

Can you write it step by step. Im losing the beginning.