Question

Which of the following are the factors of $ax+by+bx+az+ay+bz$ ?

• A. $(bxc+ay)(ax+by)$
• B. $(a+b)(2x+2y+2z)$
• C. $(x+y+z)(a+b)$
• D. $(bc+axy)(a+by)$

Answer 1

The correct option is C

$(x+y+z)(a+b)$

Consider the given expression,

$ax+by+bx+az+ay+bz$

Rearranging the terms in the given expression, we get
$=(ax+ay+az)+(bx+by+bz)$

Taking $a$ common from first three terms and $b$ common from last three terms, we get
$=a(x+y+z)+b(x+y+z)$

Taking $(x+y+z)$ common, we get
$=(x+y+z)(a+b)$

Therefore, the factors of $ax+by+bx+az+ay+bz$ are $(x+y+z)$ and $(a+b)$.

i.e., $ax+by+bx+az+ay+bz$$=(x+y+z)(a+b)$