Question

1f p =
q- . r - verify px (q + r) = (p x q) + (p x r)​

Answer 1

$\rm{p\times (q + r) = (p \times q) + (p \times r)}$

$\longrightarrow\rm{(q-r)\times (q + r) = [(q-r) \times q] + [(q-r) \times r]\quad...\:Since\:p=q-r}$

$\longrightarrow\rm{q^2-r^2 = [(q-r) \times q] + [(q-r) \times r]\quad...\:Since\:(a+b)(a-b)=a^2-b^2}$

$\longrightarrow\rm{q^2-r^2 = (q^2-qr) + (qr-r^2)}$

$\longrightarrow\rm{q^2-r^2 = q^2-qr + qr-r^2=q^2-r^2}$

$\bigstar\textrm{ Hence \rm{p\times (q + r) = (p \times q) + (p \times r)} will be true if p = q - r}$